G H Hardy's papers


Listing all of G H Hardy's papers seems an almost impossible task. We have deliberately omitted Hardy's reviews and Questions in the Educational Times. Some papers were not published in the year marked on the journal in which they appear, but in the following year, and we fear we had been inconsistent in which of the two years we give. One final apology is that, although we have put the papers in chronological order by year, we have not sorted them within a particular year. A consequence of this is that often an nnth part of a paper appears after the (n+1)(n+1)st etc.

  1. G H Hardy, On a class of definite integrals containing hyperbolic functions, Messenger of Mathematics 29 (1900), 25-42.

  2. G H Hardy, General theorems in contour integration: with some applications, Quarterly Journal of Mathematics 32 (1901), 369-384.

  3. G H Hardy, On differentiation and integration under the integral sign, Quarterly Journal of Pure and Applied Mathematics 32 (1901), 66-140.

  4. G H Hardy, Notes on some points in the integral calculus I: On the formula for integration by parts, Messenger of Mathematics 30 (1901), 185-187.

  5. G H Hardy, Notes on some points in the integral calculus II: Two general convergence theorems, Messenger of Mathematics 30 (1901), 187-190.

  6. G H Hardy, The elementary theory of Cauchy's principal values, Proceedings of the London Mathematical Society (1) 34 (1) (1902), 16-40.

  7. G H Hardy, The theory of Cauchy's principal values II: The use of principal values in some of the double limit problems of the integral calculus, Proceedings of the London Mathematical Society (1) 34 (1) (1902), 55-91.

  8. G H Hardy, On the Frullanian integral 0ϕ(axm)ψ(bxn)x(logx)pdx\large \int_{0}^\infty \Large\frac {\phi(ax^m) - \psi(bx^n)}{x}\normalsize(\log x)^p dx, Quarterly Journal of Mathematics 33 (1902), 113-144.

  9. G H Hardy, On the zeros of the integral function xsin(x)=n=1(1)n1x2n+2(2n+1)!x - \sin (x) =\large\sum_{n=1}^\infty\normalsize (-1)^{n-1}\Large\frac{x^{2n+2} }{(2n+1)!}, Messenger of Mathematics 31 (1902), 161-165.

  10. G H Hardy, Notes on some points in the integral calculus III: On the logarithmic criteria for the absolute convergence of an integral whose upper limit is infinity, Messenger of Mathematics 31 (1902), 1-6.

  11. G H Hardy, Notes on some points in the integral calculus IV: On the integral 0sinxψ(x)dx\int_{0}^\infty \sin {x} \psi(x) dx, Messenger of Mathematics 31 (1902), 6-8.

  12. G H Hardy, A new proof of Kummer's series for logΓ(a)\log \Gamma (a), Messenger of Mathematics 31 (1902), 31-33.

  13. G H Hardy, Notes on some points in the integral calculus V: On absolutely convergent integrals of functions which are infinitely often infinite, Messenger of Mathematics 31 (1902), 73-76.

  14. G H Hardy, Notes on some points in the integral calculus VI: Absolute convergence of infinite multiple integrals, Messenger of Mathematics 31 (1902), 125-128.

  15. G H Hardy, Notes on some points in the integral calculus VII: On differentiation under the integral sign, Messenger of Mathematics 31 (1902), 132-134.

  16. G H Hardy, Notes on some points in the integral calculus VIII: Absolutely convergent integrals of irregular types, Messenger of Mathematics 31 (1902), 177-183.

  17. G H Hardy and J E Littlewood, Note on the limiting values of the elliptic modular-functions, Quarterly Journal of Mathematics (2) 34 (1903), 76-86.

  18. G H Hardy, The theory of Cauchy's principal values III: Differentiation and integration of principal values, Proceedings of the London Mathematical Society (1) 35 (1) (1903), 81-107.

  19. G H Hardy, On the continuity and discontinuity of definite integrals which contain a continuous parameter, Quarterly Journal of Mathematics 34 (1903), 28-53.

  20. G H Hardy, On the zeroes of certain integral functions, Messenger of Mathematics 32 (1903), 36-45.

  21. G H Hardy, On the integral log(ax2+2bx+c)2αx2+2βx+γdx\large \int_{-\infty}^\infty \Large\frac {\log(ax^2+2bx+c)^2}{\alpha x^2+2\beta x+\gamma} \normalsize dx, Messenger of Mathematics 32 (1903), 45-50.

  22. G H Hardy, Notes on some points in the integral calculus IX: On the integral 0{Aϕ(sin2x)}ψ(x)dx\int_{0}^\infty \{A-\phi(\sin^2 x)\} \psi(x) dx, Messenger of Mathematics 32 (1903), 1-3.

  23. G H Hardy, Notes on some points in the integral calculus X: On conditionally convergent infinite multiple integrals, Messenger of Mathematics 32 (1902), 92-97.

  24. G H Hardy, Notes on some points in the integral calculus XI: Some conditionally convergent infinite double integrals, Messenger of Mathematics 32 (1903), 159-165.

  25. G H Hardy, Notes on some points in the integral calculus XII: On the operation which is the inverse of double integration, Messenger of Mathematics 32 (1903), 187-192.

  26. G H Hardy, A general theorem concerning absolutely convergent series, Proceedings of the London Mathematical Society (2) 1 (1) (1904), 285-290.

  27. G H Hardy, On the convergence of certain multiple series, Proceedings of the London Mathematical Society (2) 1 (1) (1904), 124-128.

  28. G H Hardy, A theorem concerning the infinite cardinal numbers, Quarterly Journal of Mathematics 35 (1904), 87-94.

  29. G H Hardy, On the zeros of a class of integral functions, Messenger of Mathematics (2) 34 (1904), 97-101.

  30. G H Hardy, Researches in the theory of divergent series and divergent integrals, Quarterly Journal of Mathematics 35 (1904), 22-66.

  31. G H Hardy, The asymptotic solution of certain transcendental equations, Quarterly Journal of Mathematics 35 (1904), 261-282.

  32. G H Hardy, Notes on some points in the integral calculus XIII: On differentiation under the integral sign (continued), Messenger of Mathematics 33 (1904), 62-67.

  33. G H Hardy, Notes on some points in the integral calculus XIV: Integrals whose discontinuities are everywhere dense, Messenger of Mathematics 33 (1904), 80-85.

  34. G H Hardy, On differentiation and integration of divergent series, Transactions of the Cambridge Philosophical Society 19 (3) (1904), 297-321.

  35. G H Hardy, Note on the function xe12(x2t2)dt\large \int_{x}^\infty e^{-\frac 1 2 (x^2-t^2)}\normalsize dt, Quarterly Journal of Mathematics 35 (1904), 193-207.

  36. G H Hardy, The cardinal number of a closed set of points, The Messenger of Mathematics (2) 33 (1904), 67-69.

  37. G H Hardy, Note on divergent Fourier series, The Messenger of Mathematics (2) 33 (1904), 137-144.

  38. G H Hardy, On the zeros of two classes of Taylor series, British Association Report (1904), 441-443.

  39. T J I A Bromwich and G H Hardy, Some extensions to multiple series of Abel's theorem on the continuity of power series, Proceedings of the London Mathematical Society (2) 2 (1) (1905), 161-189.

  40. G H Hardy, A method for determining a behaviour of certain classes of power series near a singular point on the circle of convergence, Proceedings of the London Mathematical Society (2) 3 (1) (1905), 381-389.

  41. G H Hardy, Note in addition to a former paper on conditionally convergent multiple series, Proceedings of the London Mathematical Society (2) 2 (1) (1905), 190-191.

  42. G H Hardy, On a class of analytic functions, Proceedings of the London Mathematical Society (2) 3 (1) (1905), 441-460.

  43. G H Hardy, On certain series of discontinuous functions connected with the modular functions, Quarterly Journal of Mathematics 36 (1905), 93-123.

  44. G H Hardy, On double Fourier series, and especially those which represent the double zeta-function with real and incommensurable parameters, Quarterly Journal of Pure and Applied Mathematics 37 (1905), 53-79.

  45. G H Hardy, On the roots of the equation 1Γ(x+1)=c\Large\frac{1}{\Gamma (x+1)}\normalsize = c, Proceedings of the London Mathematical Society (2) 2 (1) (1905), 1-7.

  46. G H Hardy, On the zeroes certain classes of integral Taylor series I: On the integral function n=0xϕ(n)(ϕ(n))!\large \sum_{n=0}^\infty \Large\frac {x^{\phi(n)}}{(\phi(n))!}, Proceedings of the London Mathematical Society (2) 2 (1) (1905), 332-339.

  47. G H Hardy, On the expression of the double zeta-function and double gamma-function in terms of elliptic functions, Transactions of the Cambridge Philosophical Society 20 (1905), 395-427.

  48. G H Hardy, On the zeroes of certain classes of integral Taylor series II: On the integral function n=0xn(n+a)2n!\large\sum_{n=0}^\infty \Large\frac {x^n}{(n+a)^2 n!} and other similar functions, Proceedings of the London Mathematical Society (2) 2 (1) (1905), 401-431.

  49. G H Hardy, Note on an integral function, The Messenger of Mathematics 34 (1905), 1-2.

  50. G H Hardy, Notes on some points in the integral calculus XV: On upper and lower integration, Messenger of Mathematics 34 (1905), 3-6.

  51. G H Hardy, Notes on some points in the integral calculus XVI: A class of conditionally convergent infinite multiple integrals, Messenger of Mathematics 34 (1905), 6-10.

  52. G H Hardy, A generalisation of Frullani's integral, Messenger of Mathematics (2) 34 (1905), 11-18.

  53. G H Hardy, On the zeroes of a class of integral functions, Messenger of Mathematics (2) 34 (1905), 97-101.

  54. G H Hardy, On certain conditionally convergent multiple series connected with the elliptic functions, Messenger of Mathematics (2) 34 (1905), 146-153.

  55. G H Hardy, On double Fourier series and especially those which represent the double zeta-function with real and incommensurable parameters, Quarterly Journal of Mathematics 37 (1) (1906), 53-79.

  56. G H Hardy, On the function Pρ(x)P_{\rho(x)}, Quarterly Journal of Mathematics 37 (1906), 146-172.

  57. G H Hardy, A formula for the prime factors of any number, Messenger of Mathematics 35 (1906), 145-146.

  58. G H Hardy, On Kummer's series for logΓ(a)\log \Gamma (a), Quarterly Journal of Mathematics 37 (1906), 49-53.

  59. G H Hardy, Some notes on certain theorems in higher trigonometry, The Mathematical Gazette (3) 56 (1906), 284-288.

  60. G H Hardy, On certain double integrals, Quarterly Journal of Mathematics 37 (1906), 360-369.

  61. G H Hardy, On the integral function Φa,α,β(z)=xn(n+a)αn+β\Phi_{a,\alpha,\beta}(z)=\large\sum\Large\frac{x^n}{(n+a)^{\alpha n + \beta}}, Quarterly Journal of Mathematics 37 (1906), 369-378.

  62. G H Hardy, Notes on some points in the integral calculus XVII: On the integration of series, Messenger of Mathematics 35 (1906), 125-130.

  63. G H Hardy, Notes on some points in the integral calculus XVIII: On some discontinuous integrals, Messenger of Mathematics 35 (1906), 158-166.

  64. G H Hardy, On the singularities of functions defined by Taylor's series: Remarks in addition to a former paper, Proceedings of the London Mathematical Society (2) 5 (1) (1907), 197-205.

  65. G H Hardy, Some theorems concerning infinite series, Mathematische Annalen. 64 (1907), 77-94.

  66. G H Hardy, On certain oscillating series, Quarterly Journal of Pure and Applied Mathematics 38 (1907), 269-288.

  67. G H Hardy, A curious imaginary curve. The Mathematical Gazette 4 (61) (1907): 14.

  68. G H Hardy, Higher Trigonometry, The Mathematical Gazette 4 (61) (1907), 13-14.

  69. G H Hardy, The line at infinity, etc., The Mathematical Gazette 4 (61) (1907), 14-15.

  70. G H Hardy, Some theorems connected with Abel's theorem on the continuity of power series, Proceedings of the London Mathematical Society (2) 4 (1) (1907), 247-265.

  71. G H Hardy, The continuum and the second number class, Proceedings of the London Mathematical Society (2) 4 (1) (1907), 10-17.

  72. G H Hardy, The singular points of certain classes of functions of several variables, Proceedings of the London Mathematical Society (2) 5 (1) (1907), 342-360.

  73. G H Hardy, Notes on some points in the integral calculus XIX: On Abel's lemma and the second theorem of the mean, Messenger of Mathematics 36 (1907), 10-13.

  74. G H Hardy, Generalisation of a theorem in the theory of divergent series, Proceedings of the London Mathematical Society (2) 6 (1) (1908), 255-264.

  75. G H Hardy, The multiplication of conditionally convergent series, Proceedings of the London Mathematical Society (2) 6 (1) (1908), 410-423.

  76. G H Hardy, Mendelian proportions in a mixed population, Science 28 (706) (1908), 49-50.

  77. G H Hardy, Further researches in the theory of divergent series and integrals, Transactions of the Cambridge Philosophical Society 21 (1908), 1-48.

  78. G H Hardy, Some multiple integrals, Quarterly Journal of Mathematics (Oxford) (2) 5 (1908), 357-375.

  79. T J l'A Bromwich and G H Hardy, The definition of an infinite integral as the limit of a finite or infinite series, The Quarterly Journal of Pure and Applied Mathematics 39 (1908), 222-240.

  80. G H Hardy, Notes on some points in the integral calculus XX: On double Frullanian integrals, Messenger of Mathematics 37 (1908), 96-103.

  81. G H Hardy, Notes on some points in the integral calculus XXI: On a conditionally convergent multiple integral, Messenger of Mathematics 37 (1908), 127-130.

  82. G H Hardy, Notes on some points in the integral calculus XXII: On double Frullanian integrals (cont.), Messenger of Mathematics 37 (1908), 154-161.

  83. G H Hardy, A note on the continuity or discontinuity of a function defined by an infinite product, Proceedings of the London Mathematical Society (2) 7 (1) (1909), 40-48.

  84. G H Hardy, On an integral equation, Proceedings of the London Mathematical Society (2) 7 (1) (1909), 445-472.

  85. G H Hardy, The theory of Cauchy's principal values IV: The integration of principal values continued with applications to the inversion of definite integrals, Proceedings of the London Mathematical Society (2) 7 (1) (1909), 181-208.

  86. G H Hardy, The integral 0sinxxdx\large \int_{0}^\infty \Large \frac {\sin x}{x}\normalsize dx, The Mathematical Gazette 5 (80) (1909), 98-103.

  87. G H Hardy, On certain definite integrals whose values can be expressed in terms of Bessel's functions, Messenger of Mathematics 38 (1909), 129-132.

  88. G H Hardy, Notes on some points in the integral calculus XXIII: On certain oscillating cases of Dirichlet's integral, Messenger of Mathematics 38 (1909), 1-8.

  89. G H Hardy, Notes on some points in the integral calculus XXIV: Oscillating cases of Dirichlet's integral (cont.), Messenger of Mathematics 38 (1909), 176-185.

  90. G H Hardy, The application to Dirichlet's series of Borel's exponential method of summation, Proceedings of the London Mathematical Society (2) 8 (1) (1910), 277-294.

  91. G H Hardy, The ordinal relations of the terms of a convergent sequence, Proceedings of the London Mathematical Society (2) 8 (1) (1910), 295-300.

  92. G H Hardy, Theorems relating to the summability and convergence of slowly oscillating series, Proceedings of the London Mathematical Society (2) 8 (1) (1910), 301-320.

  93. G H Hardy, The maximum modulus of an integral function, Quarterly Journal of Mathematics 41 (1910), 1-9.

  94. G H Hardy, On certain definite integrals considered by Airy and by Stokes, Quarterly Journal of Mathematics 41 (1910), 226-240.

  95. G H Hardy, Notes on some points in the integral calculus XXV: Absolutely convergent integrals of irregular types (cont.), Messenger of Mathematics 39 (1910), 28-32.

  96. G H Hardy, On the zeroes of the integral function xn2n2!\large \sum \Large\frac{x^{n^2}}{n^2!}, Messenger of Mathematics 39 (1910), 88-96.

  97. G H Hardy, Notes on some points in the integral calculus XXVI: On a case of term-by-term integration of an infinite series, Messenger of Mathematics 39 (1910), 136-139.

  98. G H Hardy, To find an approximation to the large positive root of the equation eex=1010x10e1010x10\large e^{e^x}\normalsize = 10^{10}x^{10}e^{10^{10}x^{10}}, The Mathematical Gazette 5 (1910), 333-334.

  99. G H Hardy, Theorems connected with Maclaurin's test for the convergence of series, Proceedings of the London Mathematical Society (2) 9 (1) (1911), 126-144.

  100. S Chapman and G H Hardy, A general view of the theory of summable series, Quarterly Journal of Mathematics 42 (1911), 181-215.

  101. G H Hardy, Fourier's double integral and the theory of divergent integrals, Transactions of the Cambridge Philosophical Society 21 (1911), 427-451.

  102. G H Hardy, Notes on some points in the integral calculus XXVII: A conditionally convergent double integral, Messenger of Mathematics 40 (1911), 44-53.

  103. G H Hardy, A class of definite integrals, Messenger of Mathematics 40 (1911), 53-54.

  104. G H Hardy, Notes on some points in the integral calculus XXVIII: A conditionally convergent double integral, Messenger of Mathematics 40 (1911), 62-69.

  105. G H Hardy, Notes on some points in the integral calculus XXIX: Two convergence theorems, Messenger of Mathematics 40 (1911), 87-91.

  106. G H Hardy, Notes on some points in the integral calculus XXX: A theorem concerning summable integrals, Messenger of Mathematics 40 (1911), 108-112.

  107. G H Hardy, Notes on some points in the integral calculus XXXI: The uniform convergence of Borel's integral, Messenger of Mathematics 40 (1911), 161-165.

  108. G H Hardy, On the multiplication of Dirichlet's series, Proceedings of the London Mathematical Society (2) 10 (1) (1912), 396-405.

  109. G H Hardy, Properties of logarithmico-exponential functions, Proceedings of the London Mathematical Society (2) 10 (1) (1912), 54-90.

  110. G H Hardy, Some results concerning the behaviour at infinity of a real and continuous solution of an algebraic differential equation of the first order, Proceedings of the London Mathematical Society (2) 10 (1) (1912), 451-468.

  111. G H Hardy and J E Littlewood, Some problems of Diophantine approximation, 5th International Congress of Mathematicians, Cambridge 1 (1912), 223-229.

  112. G H Hardy, Notes on some points in the integral calculus XXXII: On double series and double integrals, Messenger of Mathematics 41 (1912), 44-48.

  113. G H Hardy, Notes on some points in the integral calculus XXXIII: Some cases of the inversion of the order of integration, Messenger of Mathematics 41 (1912), 102-109.

  114. G H Hardy, Note on a theorem of Cesàro, Messenger of Mathematics 41 (1912), 17-22.

  115. G H Hardy, Note on Dr Vacca's series for γ\gamma, Quarterly Journal of Mathematics 43 (1912), 215-216.

  116. G H Hardy and J E Littlewood, Contributions to the arithmetic theory of series, Proceedings of the London Mathematical Society (2) 11 (1) (1913), 411-478.

  117. G H Hardy and J E Littlewood, The relations between Borel's and Cesàro's methods of summation, Proceedings of the London Mathematical Society (2) 11 (1) (1913), 1-16.

  118. G H Hardy, An extension of a theorem on oscillating series, Proceedings of the London Mathematical Society (2) 12 (1) (1913), 174-180.

  119. G H Hardy, On the summability of Fourier's series, Proceedings of the London Mathematical Society (2) 12 (1) (1913), 365-376.

  120. G H Hardy, Oscillating Dirichlet's integrals: and essay in the 'Infinitärcalcül' of Paul Du Bois-Reymond, Quarterly Journal of Mathematics 44 (1913), 1-40.

  121. G H Hardy, A theorem concerning Taylor's series, Quarterly Journal of Mathematics 44 (1913), 147-160.

  122. G H Hardy, Oscillating Dirichlet's integrals (Second Paper), Quarterly Journal of Mathematics 44 (1913), 242-263.

  123. G H Hardy, Notes on some points in the integral calculus XXXIV: Absolutely convergent integral of irregular types (cont.), Messenger of Mathematics 42 (1913), 13-18.

  124. G H Hardy, Notes on some points in the integral calculus XXXV: On an integral equation, Messenger of Mathematics 42 (1913), 89-93.

  125. G H Hardy and J E Littlewood, Tauberian theorems concerning series of positive terms, Messenger of Mathematics 42 (1913), 191-192.

  126. G H Hardy and J E Littlewood, Sur la série de Fourier d'une fonction à carré sommable, Comptes Rendus 156 (1913), 1307-1309.

  127. G H Hardy, Sur les zéros de la fonction z(s) de Riemann, Comptes Rendus 158 (1914), 1012-1014.

  128. G H Hardy and J E Littlewood, Some problems of Diophantine approximation I: The fractional part of nkθn^{k\theta}, Acta Mathematica 37 (1914), 155-191.

  129. G H Hardy and J E Littlewood, Some problems of Diophantine approximation II: The trigonometrical series associated with the elliptic θ\theta-functions, Acta Mathematica 37 (1914), 193-239.

  130. G H Hardy and J E Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coefficients are positive, Proceedings of the London Mathematical Society (2) 13 (1) (1914), 174-191.

  131. G H Hardy, Note on Lambert's series, Proceedings of the London Mathematical Society (2) 13 (1) (1914), 192-198.

  132. G H Hardy, Note in addition to a paper on Tayler's series, Quarterly Journal of Mathematics 45 (1914), 77-84.

  133. G H Hardy, A function of two variables, Quarterly Journal of Mathematics 45 (1914), 85-113.

  134. G H Hardy, Notes on some points in the integral calculus XXXVI: On the asymptotic values of certain integrals, Messenger of Mathematics 43 (1914), 9-13.

  135. G H Hardy, Notes on some points in the integral calculus XXXVII: On the region of convergence of Borel's integral, Messenger of Mathematics 43 (1914), 22-24.

  136. G H Hardy, Notes on some points in the integral calculus XXXVIII: On the definition of an analytic function by means of a definite integral, Messenger of Mathematics 43 (1914), 29-33.

  137. G H Hardy and J E Littlewood, Some theorems concerning Dirichlet's series, Messenger of Mathematics 43 (1914), 134-147.

  138. G H Hardy, The mean value of the modulus of an analytic function, Proceedings of the London Mathematical Society (2) 14 (1) (1915), 269-277.

  139. G H Hardy and J E Littlewood, New proofs of the prime-number theorem and similar theorems, Quarterly Journal of Mathematics 46 (1915), 215-219.

  140. G H Hardy, Correction of an error, Quarterly Journal of Mathematics 46 (1915), 261-262.

  141. G H Hardy, On the expression of a number as the sum of two squares, Quarterly Journal of Mathematics 46 (1915), 263-283.

  142. G H Hardy, Proof of a formula of Mr Ramanujan, Messenger of Mathematics 44 (1915), 18-21.

  143. G H Hardy, Notes on some points in the integral calculus XXXIX: Further examples of conditionally convergent infinite double integrals, Messenger of Mathematics 44 (1915), 57-63.

  144. G H Hardy, Notes on some points in the integral calculus XL: Some cases of term-by-term integration of an infinite series, Messenger of Mathematics 44 (1915), 145-149.

  145. G H Hardy, Notes on some points in the integral calculus XLI: On the convergence of certain integrals and series, Messenger of Mathematics 44 (1915), 163-166.

  146. G H Hardy, Sur le problème des diviseurs de Dirichlet, Comptes Rendus 160 (1915), 617-619.

  147. G H Hardy, Prime numbers, British Association Report (1915), 350-354.

  148. G H Hardy, Example to illustrate a point in the theory of Dirichlet's series, The Tôhoku Mathematics Journal 8 (1915), 59-66.

  149. G H Hardy, The definition of a complex number, The Mathematical Gazette 8 (1915), 48-49.

  150. G H Hardy and J E Littlewood, Some problems of Diophantine approximation, Acta Mathematica vol. 37, 231, Acta Mathematica 41 (1916), 196.

  151. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: A remarkable trigonometrical series, Proceedings of the National Academy of Sciences of the United States of America 2 (10) (1916), 583-586.

  152. G H Hardy and J E Littlewood, Theorems concerning the summability of series by Borel's exponential method, Rendiconti Del Circolo Matematico Di Palermo 41 (1916), 36-53.

  153. G H Hardy, Weierstrass's non-differentiable function, Transactions of the American Mathematical Society 17 (1916), 301-325.

  154. G H Hardy, The application of Abel's method of summation to Dirichlet's series, Quarterly Journal of Mathematics 47 (1916), 176-192.

  155. G H Hardy, On Dirichlet's divisor problem, Proceedings of the London Mathematical Society (2) 15 (1) (1916), 1-25.

  156. G H Hardy, The average order of the arithmetical functions P(x)P(x) and Δ(x)\Delta (x), Proceedings of the London Mathematical Society (2) 15 (1) (1916), 192-213.

  157. G H Hardy, Sur la sommation des séries de Dirichlet, Comptes Rendus 162 (1916), 463-465.

  158. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: The series e(λn)\sum e(\lambda_n) and the distribution of the points (λnα)(\lambda_{n \alpha }), Proceedings of the National Academy of Sciences 3 (1916), 84-88.

  159. G H Hardy, Asymptotic formulae in combinatorial analysis, Quatrième Congrès Mathématiciens, Scandinaves (1916), 45-53.

  160. G H Hardy, Further remarks on the integral 0sinxxdx\large \int_{0}^\infty \Large\frac {\sin x}{x}\normalsize dx, The Mathematical Gazette 8 (1916), 301-303.

  161. G H Hardy, The second theorem of consistency for summable series, Proceedings of the London Mathematical Society (2) 15 (1) (1916), 72-88.

  162. G H Hardy and S Ramanujan, Une formule asymptotique pour le nombre des partitions de nn, Comptes rendus 164 (1917), 35-38.

  163. G H Hardy and S Ramanujan, Asymptotic formula for the distribution of integers of various types, Proceedings of the London Mathematical Society (2) 16 (1) (1917), 112-132.

  164. G H Hardy, On a theorem of Mr G Pólya, Proceedings of the Cambridge Philosophical Society 19 (1917), 60-63.

  165. G H Hardy, On the convergence of certain multiple series, Proceedings of the Cambridge Philosophical Society 19 (1917), 86-95.

  166. G H Hardy, Notes on some points in the integral calculus XLII: On Weierstrass's singular integral, and on a theorem of Lerch, Messenger of Mathematics 46 (1917), 43-48.

  167. G H Hardy, Notes on some points in the integral calculus XLIII: On the asymptotic value of a definite integral, and the coefficient in a power series, Messenger of Mathematics 46 (1917), 70-73.

  168. G H Hardy, Notes on some points in the integral calculus XLIV: On certain multiple integrals and series which occur in the analytic theory of numbers, Messenger of Mathematics 46 (1917), 104-107.

  169. G H Hardy, Notes on some points in the integral calculus XLV: On a point in the theory of Fourier series, Messenger of Mathematics 46 (1917), 146-149.

  170. G H Hardy, Notes on some points in the integral calculus XLVI: On Stieltjes' 'probleme des moments', Messenger of Mathematics 46 (1917), 175-182.

  171. G H Hardy and J E Littlewood, Sur la convergence des séries de Fourier et des séries de Taylor, Comptes Rendus 165 (1917), 1047-1049.

  172. G H Hardy, Mr S Ramanujan's mathematical work in England, Journal of the Indian Mathematical Society 9 (1917), 30-45.

  173. G H Hardy and J E Littlewood, Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes, Acta Mathematica 41 (1918), 119-196.

  174. G H Hardy and S Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society (2) 17 (1) (1918), 75-115.

  175. G H Hardy and S Ramanujan, On the coefficients in the expansion of certain modular functions, Proceedings of the Royal Society (A) 95 (1918), 144-155.

  176. G H Hardy, Sir George Stokes and the concept of uniform convergence, Proceedings of the Cambridge Philosophical Society 19 (1918), 148-156.

  177. G H Hardy and J E Littlewood, On the Fourier series of a bounded function, Proceedings of the London Mathematical Society (2) 17 (1) (1918), xiii-xv.

  178. G H Hardy, Notes on some points in the integral calculus XLVII: On Stieltjes' 'probleme des moments' (cont.), Messenger of Mathematics 47 (1918), 81-88.

  179. G H Hardy, Notes on some points in the integral calculus XLVIII: On some properties of integrals of fractional order, Messenger of Mathematics 47 (1918), 145-150.

  180. G H Hardy, Notes on some points in the integral calculus XLIX: On Mellin's inversion formula, Messenger of Mathematics 47 (1918), 178-184.

  181. G H Hardy, Note on an expression of Lambert's series as a definite integral, Messenger of Mathematics 47 (1918), 190-192.

  182. G H Hardy, On the representation of a number as the sum of any number of squares, and in particular of five or seven, Proceedings of the National Academy of Sciences 4 (1918), 189-193.

  183. G H Hardy and J E Littlewood, Note on Messrs Shah and Wilson's paper entitled: 'On an empirical formula connected with Goldbach's theorem, Proceedings of the Cambridge Philosophical Society 19 (1919), 245-254.

  184. G H Hardy, Notes on some points in the integral calculus L: On the integral of Stieltjes and the formula for integration by parts, Messenger of Mathematics 48 (1919), 90-100.

  185. G H Hardy, Notes on some points in the integral calculus LI: On Hilbert's double-series theorem, and some connected theorems concerning the convergence of infinite series and integrals, Messenger of Mathematics 48 (1919), 107-112.

  186. G H Hardy, A problem of Diophantine approximation, Journal of the Indian Mathematical Society 11 (1919), 162-166.

  187. G H Hardy, Additional note on two problems in the analytic theory of numbers, Proceedings of the London Mathematical Society (2) 18 (1) (1920), 201-204.

  188. G H Hardy and J E Littlewood, Abel's theorem and its converse, Proceedings of the London Mathematical Society (2) 18 (1) (1920), 205-235.

  189. G H Hardy, Note on a theorem of Hilbert, Mathematische Zeitschrift 6 (1920), 314-317.

  190. G H Hardy, On the representation of a number as the sum of any number of squares, and in particular of five, Transactions of the American Mathematical Society 21 (1920), 255-284.

  191. G H Hardy, On two theorems of F Carlson and S Wigert, Acta Mathematica 42 (1920), 327-339.

  192. G H Hardy and J E Littlewood, Some problems of "partitio numerorum" I: A new solution of Waring's Problem, Göttinger Nachrichten (1920), 33-54.

  193. G H Hardy and S Ramanujan, The normal number of rime factors of a number n, Quarterly Journal of Mathematics 48 (1920), 76-92.

  194. G H Hardy and J E Littlewood, A new solution of Waring's problem, Quarterly Journal of Mathematics 48 (1920), 272-293.

  195. G H Hardy, Notes on some points in the integral calculus LII: On some definite integrals considered by Mellin, Messenger of Mathematics 49 (1920), 85-91.

  196. G H Hardy, Notes on some points in the integral calculus LIII: On certain criteria for the convergence of the Fourier series of a continuous function, Messenger of Mathematics 49 (1920), 149-155.

  197. G H Hardy and J E Littlewood, On a Tauberian theorem for Lambert's series, and some fundamental theorems in the analytic theory of numbers, Proceedings of the London Mathematical Society (2) 19 (1) (1921), 21-29.

  198. G H Hardy and J E Littlewood, Some problems of "partitio numerorum" II: Proof that every large number is the sum of at most 21 biquadrates, Mathematische Zeitschrift 9 (1921), 14-27.

  199. G H Hardy and J E Littlewood, The zeros of Riemann's zeta-function on the critical line, Mathematische Zeitschrift 10 (1921), 283-317.

  200. G H Hardy, Note on Ramanujan's trigonometrical function cq(n)c_{q(n)}, and certain series of arithmetical functions, Proceedings of the Cambridge Philosophical Society 20 (1921), 263-271.

  201. G H Hardy, A theorem concerning summable series, Proceedings of the Cambridge Philosophical Society 20 (1921), 304-307.

  202. G H Hardy, A convergence theorem, Proceedings of the London Mathematical Society (2) 19 (1) (1921), vi-vii.

  203. G H Hardy, Notes on some points in the integral calculus LIV: Further notes on Mellin's inversion formulae, Messenger of Mathematics 50 (1921), 165-171.

  204. G H Hardy, Obituary: Srinivasa Ramanujan, Proceedings of the London Mathematical Society (2) 19 (1) (1921), xl-lviii.

  205. G H Hardy, Obituary: Srinivasa Ramanujan, Proceedings of the Royal Society (A) 99 (1921), xiii-xxix.

  206. G H Hardy, Obituary: Srinivasa Ramanujan, Nature 105 (1921), 494-495.

  207. G H Hardy, Obituary: Camille Jordan, Proceedings of the Royal Society (A) 104 (1922), xxiii-xxvi.

  208. G H Hardy, Goldbach's theorem, Matematisk Tidsskrift B (1922), 1-16.

  209. G H Hardy, A new proof of the functional equation for the zeta-function, Matematisk Tidsskrift B (1922), 71-73.

  210. G H Hardy and J E Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Mathematica 44 (1922), 1-70.

  211. G H Hardy and J E Littlewood, Some problems of 'Partitio Numerorum' IV: The singular series in Waring's Problem and the value of the number G(k)G(k), Mathematische Zeitschrift 12 (1922), 161-188.

  212. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: The lattice-points of a right-angled triangle II, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 (1922), 211-248.

  213. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: A further note on the trigonometrical series associated with the elliptic theta-functions, Proceedings of the Cambridge Philosophical Society (2) 21 (1) (1922), 1-5.

  214. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: The lattice points of a right-angled triangle, Proceedings of the London Mathematical Society (2) 20 (1) (1922), 15-36.

  215. T Carleman and G H Hardy, Fourier's series and analytic functions, Proceedings of the Royal Society (A) 101 (1922), 124-133.

  216. G H Hardy and J E Littlewood, Summation of a certain multiple series, Proceedings of the London Mathematical Society (2) 20 (1) (1922), xxx.

  217. G H Hardy, Notes on some points in the integral calculus LV: On the integration of Fourier series, Messenger of Mathematics 51 (1922), 186-192.

  218. G H Hardy, The theory of numbers, British Association Report (1922), 16-24.

  219. G H Hardy and J E Littlewood, The approximate functional equation in the theory of the zeta-function, with applications to the divisor-problems of Dirichlet and Piltz, Proceedings of the London Mathematical Society (2) 21 (1) (1923), 39-74.

  220. G H Hardy, A chapter from Ramanujan's notebook, Proceedings of the Cambridge Philosophical Society (2) 21 (1) (1923), 492-503.

  221. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: The analytic character of the sum of a Dirichlet's series considered by Hecke, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 (1923), 57-68.

  222. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: The analytic properties of certain Dirichlet's series associated with the distribution of numbers to modulus unity, Transactions of the Cambridge Philosophical Society 22 (1923), 519-533.

  223. G H Hardy, Notes on some points in the integral calculus LVI: On Fourier series and Fourier's integral, Messenger of Mathematics 52 (1923), 49-53.

  224. G H Hardy and J E Littlewood, Abel's theorem and its converse (II), Proceedings of the London Mathematical Society (2) 22 (1) (1924), 254-269.

  225. G H Hardy and J E Littlewood, Solution of the Cesàro summability problem for power-series and Fourier series, Mathematische Zeitschrift 19 (1924), 67-96.

  226. G H Hardy and J E Littlewood, Some problems of 'Partitio numerorum' (V): A further contribution to the study of Goldbach's problem, Proceedings of the London Mathematical Society (2) 22 (1) (1924), 46-56.

  227. G H Hardy, Some formulae of Ramanujan, Proceedings of the London Mathematical Society (2) 22 (1) (1924), xii-xiii.

  228. G H Hardy and J E Littlewood, Note on a theorem concerning Fourier series, Proceedings of the London Mathematical Society (2) 22 (1) (1924), xviii-xix.

  229. G H Hardy and J E Littlewood, The equivalence of certain integral means, Proceedings of the London Mathematical Society (2) 22 (1) (1924), xl-xliii.

  230. G H Hardy, Notes on some points in the integral calculus LVII: On Fourier transforms, Messenger of Mathematics 53 (1924), 135-142.

  231. G H Hardy and E Landau, The lattice points of a circle, Proceedings of the Royal Society (A) 105 (1924), 244-258.

  232. G H Hardy and J E Littlewood, Some problems of 'Partitio numerorum' (VI): Further researches in Waring's Problem, Mathematische Zeitschrift 23 (1925), 1-37.

  233. G H Hardy and E C Titchmarsh, Solutions of some integral equations considered by Bateman, Kapteyn, Littlewood, and Milne, Proceedings of the London Mathematical Society (2) 23 (1) (1925), 1-26.

  234. G H Hardy, The lattice points of a circle, Proceedings of the Royal Society (A) 107 (1925), 623-635.

  235. G H Hardy, What is geometry?, The Mathematical Gazette 12 (1925), 309-316.

  236. G H Hardy and J E Littlewood, Some problems of Diophantine approximation: An additional note on the trigonometrical series associated with the elliptic theta-functions, Acta Mathematica 47 (1925), 189-198.

  237. G H Hardy and J E Littlewood, S A theorem concerning series of positive terms, with applications to the theory of functions, Meddelelser Kobenhavn 7 (4) (1925).

  238. G H Hardy, Note on a theorem of Hilbert concerning series of positive terms, Proceedings of the London Mathematical Society (2) 23 (1) (1925), lxi-lxiii.

  239. G H Hardy, Notes on some points in the integral calculus LVIII: On Hilbert transforms, Messenger of Mathematics 54 (1925), 20-27.

  240. G H Hardy, Notes on some points in the integral calculus LIX: On Hilbert transforms (cont.), Messenger of Mathematics 54 (1925), 81-88.

  241. G H Hardy, Notes on some points in the integral calculus LX: An inequality between integrals, Messenger of Mathematics 54 (1925), 150-156.

  242. G H Hardy, A definite integral which occurs in physical optics, Proceedings of the London Mathematical Society (2) 24 (1) (1926), xxx-xxxi.

  243. G H Hardy and J E Littlewood, Some properties of fractional integrals, Proceedings of the London Mathematical Society (2) 24 (1) (1926), xxxvii-xli.

  244. G H Hardy, Note on the inversion of a repeated integral, Proceedings of the London Mathematical Society (2) 24 (1) (1926), l-li.

  245. G H Hardy and J E Littlewood, A further note on the converse of Abel's theorem, Proceedings of the London Mathematical Society (2) 25 (1) (1926), 219-236.

  246. G H Hardy and J E Littlewood, Notes on the theory of series I: Two theorems concerning Fourier series, Journal of the London Mathematical Society (1) 1 (1) (1926), 19-25.

  247. G H Hardy and J E Littlewood, Notes on the theory of series II: The Fourier series of a positive function, Journal of the London Mathematical Society (1) 1 (3) (1926), 134-138.

  248. G H Hardy and J E Littlewood, The allied series of a Fourier series, Proceedings of the London Mathematical Society (2) 24 (1) (1926), 211-246.

  249. G H Hardy, A theorem concerning harmonic functions, Journal of the London Mathematical Society (1) 1 (3) (1926), 130-131.

  250. G H Hardy, J E Littlewood and G Pólya, The maximum of a certain bilinear form, Proceedings of the London Mathematical Society (2) 25 (1) (1926), 265-282.

  251. S Bochner and G H Hardy, Notes on two theorems of Norbert Wiener, Journal of the London Mathematical Society (1) 1 (4) (1926), 240-244.

  252. G H Hardy and J E Littlewood, Some new properties of Fourier constants, Mathematische Annalen 97 (1926), 159-209.

  253. G H Hardy, Notes on some points in the integral calculus LXI: On the term by term integration of a series of Bessel functions, Messenger of Mathematics 55 (1926), 140-144.

  254. G H Hardy, The case against the Mathematical Tripos, The Mathematical Gazette 13 (1926), 61-71.

  255. G H Hardy and J E Littlewood, Elementary theorems concerning power series with positive coefficients and moment constants of positive functions, Journal für die Reine und Angewandte Mathematik 157 (1927), 141-158.

  256. G H Hardy and J E Littlewood, Notes on the theory of series (V): On Parseval's theorem, Proceedings of the London Mathematical Society (2) 26 (1) (1927), 287-294.

  257. G H Hardy and J E Littlewood, Notes on the theory of series (IV): On the strong summability of Fourier series, Proceedings of the London Mathematical Society (2) 26 (1) (1927), 273-286.

  258. G H Hardy and J E Littlewood, Notes on the theory of series (VI): Two inequalities, Journal of the London Mathematical Society (1) 2 (3) (1927), 196-201.

  259. G H Hardy and J E Littlewood, Notes on the theory of series (III): On the summability of the Fourier series of a nearly continuous function, Mathematical Proceedings of the Cambridge Philosophical Society 23 (1927), 681-684.

  260. G H Hardy, Note on a theorem of Mertens, Journal of the London Mathematical Society (1) 2 (2) (1927), 70-72.

  261. G H Hardy, Note on Ramanujan's arithmetical function τ(n)\tau(n), Mathematical Proceedings of the Cambridge Philosophical Society 23 (1927), 675-680.

  262. G H Hardy, Note on the multiplication of series, Journal of the London Mathematical Society (1) 2 (3) (1927), 169-171.

  263. G H Hardy, A E Ingham and G Pólya, Theorems concerning mean values of analytic functions, Proceedings of the Royal Society (A) 113 (1927), 542-569.

  264. G H Hardy, Notes on some points in the integral calculus LXII: A singular integral, Messenger of Mathematics 56 (1927), 10-16.

  265. G H Hardy, Notes on some points in the integral calculus LXIII: Some further applications of Mellin's inversion formula, Messenger of Mathematics 56 (1927), 186-192.

  266. G H Hardy and J E Littlewood, A convergence criterion for Fourier series, Mathematische Zeitschrift 28 (1928), 612-634.

  267. G H Hardy and J E Littlewood, A theorem in the theory of summable divergent series, Proceedings of the London Mathematical Society (2) 27 (1) (1928), 327-348.

  268. G H Hardy, A E Ingham and G Pólya, Notes on moduli and mean values, Proceedings of the London Mathematical Society (2) 27 (1) (1928), 401-409.

  269. G H Hardy and J E Littlewood, Notes on the theory of series (VII): On Young's convergence criterion for Fourier series, Proceedings of the London Mathematical Society (2) 28 (1) (1928), 301-311.

  270. G H Hardy and J E Littlewood, Notes on the theory of series (X): Some more inequalities, Journal of the London Mathematical Society (1) 3 (4) (1928), 294-299.

  271. G H Hardy and J E Littlewood, Notes on the theory of series (IX): On the absolute convergence of Fourier series, Journal of the London Mathematical Society (1) 3 (4) (1928), 250-253.

  272. G H Hardy and J E Littlewood, Notes on the theory of series (VIII): An inequality, Journal of the London Mathematical Society (1) 3 (2) (1928), 105-110.

  273. G H Hardy, Obituary: Gösta Mittag-Leffler, Journal of the London Mathematical Society (1) 3 (2) (1928), 156-160.

  274. G H Hardy, Obituary: Gösta Mittag-Leffler, Proceedings of the Royal Society (A) 119 (1928), v-viii.

  275. G H Hardy and J E Littlewood, Some problems of 'Partitio numerorum' (VIII): The number ì(k) in Waring's problem, Proceedings of the London Mathematical Society (2) 28 (1) (1928), 518-542.

  276. G H Hardy, A theorem concerning trigonometrical series, Journal of the London Mathematical Society (1) 3 (1) (1928), 12-13.

  277. G H Hardy, Addenda and corrigenda, Proceedings of the London Mathematical Society (2) 28 (1) (1928), 553-553.

  278. G H Hardy, Remarks on three recent notes in the Journal, Journal of the London Mathematical Society (1) 3 (3) (1928), 166-169.

  279. G H Hardy and J E Littlewood, Some properties of fractional integrals I, Mathematische Zeitschrift 27 (1928), 565-606.

  280. G H Hardy, Notes on some points in the integral calculus LXIV: Further inequalities between integrals, Messenger of Mathematics 57 (1928), 12-16.

  281. G H Hardy, Notes on some points in the integral calculus LXV: A discontinuous integral, Messenger of Mathematics 57 (1928), 113-120.

  282. G H Hardy, A formula of Rananujan, Journal of the London Mathematical Society (1) 3 (3) (1928), 238-240.

  283. G H Hardy and J E Littlewood, A point in the theory of conjugate functions, Journal of the London Mathematical Society (1) 4 (4) (1929), 242-245.

  284. G H Hardy and J E Littlewood, The approximate functional equations for ζ(s)\zeta(s) and ζ2(s)\zeta^{2}(s), Proceedings of the London Mathematical Society (2) 29 (1) (1929), 81-97.

  285. G H Hardy, Prolegomena to a chapter on inequalities (Presidential Address), Journal of the London Mathematical Society (1) 4 (3) (1929), 61-78.

  286. G H Hardy, An introduction to the theory of numbers, Bulletin of the American Mathematical Society 35 (1929), 778-818.

  287. G H Hardy, Remarks in addition to Dr Widder's note on inequalities, Journal of the London Mathematical Society (1) 4 (3) (1929), 199-202.

  288. G H Hardy and E C Titchmarsh, Solution of an integral equation, Journal of the London Mathematical Society (1) 4 (4) (1929), 300-304.

  289. G H Hardy, Notes on some points in the integral calculus LXVI: The arithmetic mean of a Fourier constant, Messenger of Mathematics 58 (1929), 50-52.

  290. G H Hardy, Notes on some points in the integral calculus LXVII: The repeated integral which occurs in the theory of conjugate functions, Messenger of Mathematics 58 (1929), 53-58.

  291. G H Hardy, Notes on some points in the integral calculus LXVIII: The limit of an integral mean value, Messenger of Mathematics 58 (1929), 115-120.

  292. G H Hardy, Notes on some points in the integral calculus LXIX: On asymptotic values of Fourier constants, Messenger of Mathematics 58 (1929), 130-135.

  293. G H Hardy, J E Littlewood and G Pólya, Some simple inequalities satisfied by convex functions, Messenger of Mathematics 58 (1929), 145-152.

  294. G H Hardy, Mathematical proof, Mind 38 (1929), 1-25.

  295. G H Hardy, Obituary: James Whitbread Lee Glaisher, Messenger of Mathematics 58 (1929), 159-160.

  296. G H Hardy, Obituary: Thomas John l'Anson Bromwich, Journal of the London Mathematical Society (1) 5 (1930), 209-220.

  297. G H Hardy, Obituary: Thomas John l'Anson Bromwich, Proceedings of the Royal Society (A) 129 (1930), i-x.

  298. G H Hardy and J E Littlewood, A maximal theorem with function-theoretic applications, Acta Mathematica 54 (1930), 81-116.

  299. G H Hardy and J E Littlewood, Notes on the theory of series (XI): On Tauberian theorems, Proceedings of the London Mathematical Society (2) 30 (1) (1930), 23-37.

  300. G H Hardy and J E Littlewood, Notes on the theory of series (XII): On certain inequalities connected with the calculus of variations, Journal of the London Mathematical Society (1) 5 (1) (1930), 34-39.

  301. G H Hardy, Prolegomena to a chapter on inequalities (Presidential Address) addenda, Journal of the London Mathematical Society (1) 5 (3) (1930), 80.

  302. G H Hardy and E C Titchmarsh, Additional note on certain integral equations, Proceedings of the London Mathematical Society (2) 30 (1) (1930), 95-106.

  303. G H Hardy and E C Titchmarsh, Self-reciprocal functions, Quarterly Journal of Mathematics os-1 (1) (1930), 196-231.

  304. G H Hardy, Mathematics, The Oxford Magazine 48 (5 June 1930), 819-821.

  305. G H Hardy and J E Littlewood, Notes on the theory of series (XVI): Two Tauberian theorems, Journal of the London Mathematical Society (1) 6 (4) (1931), 281-286.

  306. G H Hardy and J E Littlewood, Notes on the theory of series (XV): On the series conjugate to the Fourier series of a bounded function, Journal of the London Mathematical Society (1) 6 (4) (1931), 278-281.

  307. G H Hardy and J E Littlewood, Notes on the theory of series (XIV): An additional note on the summability of Fourier series, Journal of the London Mathematical Society (1) 6 (1) (1931), 9-12.

  308. G H Hardy and J E Littlewood, Notes on the theory of series (XIII): Some new properties of Fourier constants, Journal of the London Mathematical Society (1) 6 (1) (1931), 3-9.

  309. G H Hardy, Some theorems concerning trigonometrical series of a special type, Proceedings of the London Mathematical Society (2) 32 (1) (1931), 441-448.

  310. G H Hardy, The summability of a Fourier series by logarithmic means, Quarterly Journal of Mathematics os-2 (1) (1931), 107-112.

  311. G H Hardy and E C Titchmarsh, A note on Parseval's theorem for Fourier transforms, Journal of the London Mathematical Society (1) 6 (1) (1931), 44-48.

  312. G H Hardy and J E Littlewood, Some properties of conjugate functions, Journal für die Reine und Angewandte Mathematik 167 (1931), 405-423.

  313. G H Hardy and J E Littlewood, An additional note on Parseval's theorem, Mathematische Zeitschrift 34 (1932), 634-636.

  314. G H Hardy and J E Littlewood, Notes on the theory of series (XVII): Some new convergence criteria for Fourier series, Journal of the London Mathematical Society (1) 7 (4) (1932), 252-256.

  315. G H Hardy and J E Littlewood, Some integral inequalities connected with the calculus of variations, Quarterly Journal of Mathematics os-3 (1) (1932), 241-252.

  316. G H Hardy and J E Littlewood, Some new cases of Parseval's theorem, Mathematische Zeitschrift 34 (1932), 620-633.

  317. G H Hardy and J E Littlewood, Some properties of fractional integrals II, Mathematische Zeitschrift 34 (1932), 403-439.

  318. G H Hardy, On Hilbert transforms, Quarterly Journal of Mathematics os-3 (1) (1932), 102-112.

  319. G H Hardy, Summation of a series of polynomials of Laguerre, Journal of the London Mathematical Society (1) 7 (2) (1932), 138-139.

  320. G H Hardy and E C Titchmarsh, An integral equation, Mathematical Proceedings of the Cambridge Philosophical Society 28 (1932), 165-173.

  321. G H Hardy and E C Titchmarsh, Formulae connecting different classes of self-reciprocal functions, Proceedings of the London Mathematical Society (2) 33 (1) (1932), 225-232.

  322. G H Hardy, A theorem concerning Fourier transforms, Journal of the London Mathematical Society (1) 8 (3) (1933), 227-231.

  323. G H Hardy, The constants of certain inequalities, Journal of the London Mathematical Society (1) 8 (2) (1933), 114-119.

  324. G H Hardy and E C Titchmarsh, A class of Fourier kernels, Proceedings of the London Mathematical Society (2) 35 (1) (1933), 116-155.

  325. G H Hardy and J E Littlewood, Some more integral inequalities, The Tôhoku Mathematical Journal 37 (1933), 151-159.

  326. G H Hardy and J E Littlewood, Bilinear forms bounded in space [p,q][p, q], Quarterly Journal of Mathematics os-5 (1) (1934), 241-254.

  327. G H Hardy and J E Littlewood, Theorems concerning Cesaro means of power series, Proceedings of the London Mathematical Society (2) 36 (1) (1934), 516-531.

  328. G H Hardy, On the summability of series by Borel's and Mittag-Leffler's methods, Journal of the London Mathematical Society (1) 9 (2) (1934), 153-157.

  329. G H Hardy and E M Wright, Leudesdorf's extension of Wolstenholme's theorem, Journal of the London Mathematical Society (1) 9 (1) (1934), 38-41.

  330. G H Hardy and E M Wright, Leudesdorf's extension of Wolstenholme's theorem - corrigendum, Journal of the London Mathematical Society (1) 9 (1) (1934), 240.

  331. G H Hardy and J E Littlewood, Some new convergence criteria for Fourier series, Annali Pisa (2) 3 (1934), 53-62.

  332. G H Hardy and J E Littlewood, A problem in elementary probability, Mathematical Gazette 18 (1934), 195.

  333. G H Hardy, The J-type and the S-type among mathematicians, Nature 134 (1934), 250.

  334. G H Hardy, Obituary: Raymond Edward Alan Christopher Paley, Journal of the London Mathematical Society (1) 9 (1) (1934), 75-80.

  335. G H Hardy, Obituary: Ernest William Hobson, Journal of the London Mathematical Society (1) 9 (1) (1934), 225-237.

  336. G H Hardy, Obituary: Ernest William Hobson, Obituary Notices of Fellows of the Royal Society (1934), 237-249.

  337. G H Hardy, Obituary: Ernest William Hobson, Nature 133 (1934), 938-939.

  338. G H Hardy and J E Littlewood, Notes on the theory of series (XIX): A problem concerning majorants of Fourier series, Quarterly Journal of Mathematics os-6 (1) (1935), 304-315.

  339. G H Hardy and J E Littlewood, Notes on the Theory of Series (XVIII): On the convergence of Fourier series, Mathematical Proceedings of the Cambridge Philosophical Society 31 (1935), 317-323.

  340. G H Hardy, E Landau and J E Littlewood, Some inequalities satisfied by the integrals or derivatives of real or analytic functions, Mathematische Zeitschrift 39 (1935), 677-695.

  341. G H Hardy, Second note on a theorem of Mertens, Journal of the London Mathematical Society (1) 10 (1) (1935), 91-94.

  342. G H Hardy, Some identities satisfied by infinite series, Journal of the London Mathematical Society (1) 10 (1) (1935), 217-220.

  343. G H Hardy, The resultant of two Fourier kernels, Mathematical Proceedings of the Cambridge Philosophical Society 31 (1935), 1-6.

  344. G H Hardy, Remarks on some points in the theory of divergent series, Annals of Mathematics (2) 36 (1935), 167-181.

  345. G H Hardy and J E Littlewood, An inequality, Mathematische Zeitschrift 40 (1935), 1-40.

  346. G H Hardy and J E Littlewood, The strong summability of Fourier series, Fundamenta Mathematicae 25 (1935), 162-189.

  347. G H Hardy and J E Littlewood, Notes on the theory of series (XX): On Lambert series, Proceedings of the London Mathematical Society (2) 41 (4) (1936), 257-270.

  348. G H Hardy and J E Littlewood, Some more theorems concerning Fourier series and Fourier power series, Duke Mathematical Journal 2 (1936), 354-382.

  349. G H Hardy, A note on two inequalities, Journal of the London Mathematical Society (1) 11 (3) (1936), 167-170.

  350. G H Hardy and E C Titchmarsh, New solution of an integral equation, Proceedings of the London Mathematical Society (2) 41 (4) (1936), 1-15.

  351. G H Hardy and J E Littlewood, Notes on the theory of series (XXI): Generalizations of a theorem of Paley, Quarterly Journal of Mathematics os-8 (1) (1937), 161-171.

  352. G H Hardy, A formula of Ramanujan in the theory of primes, Journal of the London Mathematical Society (1) 12 (1) (1937), 94-98.

  353. G H Hardy, Another formula of Ramanujan, Journal of the London Mathematical Society (1) 12 (4) (1937), 314-318.

  354. G H Hardy and N Levinson, Inequalities satisfied by a certain definite integral, Bulletin of the American Mathematical Society 43 (1937), 709-716.

  355. G H Hardy, On a theorem of Paley and Wiener, Mathematical Proceedings of the Cambridge Philosophical Society 33 (1937), 1-5.

  356. G H Hardy, Ramanujan and the theory of Fourier transforms, Quarterly Journal of Mathematics os-8 (1) (1937), 245-254.

  357. G H Hardy, The Indian mathematician Ramanujan, American Mathematical Monthly 44 (1937), 137-155.

  358. G H Hardy, A further note on Ramanujan's arithmetical function τ(n)\tau(n), Mathematical Proceedings of the Cambridge Philosophical Society 34 (1938), 309-315.

  359. G H Hardy and H Heilbronn, Obituary: Edmund Landau, Journal of the London Mathematical Society 13 (4) (1938), 302-310.

  360. G H Hardy, A note on a differential equation, Mathematical Proceedings of the Cambridge Philosophical Society 35 (1939), 652-653.

  361. G H Hardy, Notes on special systems of orthogonal functions (II): On functions orthogonal with respect to their own zeros, Journal of the London Mathematical Society (1) 14 (1) (1939), 37-44.

  362. G H Hardy, Notes on special systems of orthogonal functions (I): The boundedness of the generalized Laguerre system, Journal of the London Mathematical Society (1) 14 (1) (1939), 34-36.

  363. G H Hardy, Notes on special systems of orthogonal Functions (III): A System of orthogonal polynomials, Mathematical Proceedings of the Cambridge Philosophical Society 36 (1940), 1-8.

  364. G H Hardy, Mathematics in war-time, Eureka 1 (3) (1940), 5-8.

  365. G H Hardy and J E Littlewood, Theorems concerning mean values of analytic or harmonic functions, Quarterly Journal of Mathematics os-12 (1) (1941), 221-256.

  366. G H Hardy, Note on a divergent series, Mathematical Proceedings of the Cambridge Philosophical Society 37 (1941), 1-8.

  367. G H Hardy, Notes on special systems of orthogonal functions (IV): The orthogonal functions of Whittaker's cardinal series, Mathematical Proceedings of the Cambridge Philosophical Society 37 (1941), 331-348.

  368. G H Hardy, A double integral, Journal of the London Mathematical Society (1) 16 (1) (1941), 89-94.

  369. G H Hardy, Note on Lebesgue's constants in the theory of Fourier series, Journal of the London Mathematical Society (1) 17 (1) (1942), 4-13.

  370. G H Hardy, Obituary: William Henry Young, Journal of the London Mathematical Society (1) 17 (1) (1942), 218-237.

  371. G H Hardy, Obituary: William Henry Young, Nature 150 (1942), 227.

  372. G H Hardy, Obituary: William Henry Young, Obituary Notices of Fellows of the Royal Society 4 (1943), 307-323.

  373. G H Hardy, Obituary: David Hilbert, Journal of the London Mathematical Society (1) 18 (1) (1943), 191-192.

  374. G H Hardy, Obituary: Henri Léon Lebesgue, Nature 152 (1943), 685.

  375. G H Hardy and J E Littlewood, Notes on the theory of series (XXII): On the Tauberian theorem for Borel summability, Journal of the London Mathematical Society (1) 18 (4) (1943), 194-200.

  376. G H Hardy and W W Rogosinski, Notes on Fourier series (I): On sine series with positive coefficients, Journal of the London Mathematical Society (1) 18 (4) (1943), 50-57.

  377. G H Hardy and W W Rogosinski, Notes on Fourier series (II): On the Gibbs phenomenon, Journal of the London Mathematical Society (1) 18 (2) (1943), 83-87.

  378. G H Hardy, An inequality for Hausdorff means, Journal of the London Mathematical Society (1) 18 (1) (1943), 46-50.

  379. G H Hardy and J E Littlewood, Note on the theory of series (XXIII): On the partial sums of Fourier series, Mathematical Proceedings of the Cambridge Philosophical Society 40 (1944), 103-107.

  380. G H Hardy, Note on the multiplication of series by Cauchy's rule, Mathematical Proceedings of the Cambridge Philosophical Society 40 (1944), 251-252.

  381. G H Hardy and W W Rogosinski, Notes on Fourier series (III): Asymptotic formulae for the sums of certain trigonometrical series, Quarterly Journal of Mathematics os-16 (1) (1945), 49-58.

  382. G H Hardy, Riemann's form of Taylor's series, Journal of the London Mathematical Society (1) 20 (1) (1945), 48-57.

  383. G H Hardy and N Aronszajn, Properties of a class of double integrals, Annals of Mathematics (2) 46 (1945), 220-241.

  384. G H Hardy, A mathematical theorem about golf, Mathematical Gazette 29 (1945), 226-227.

  385. H S Carslaw and G H Hardy, Obituary: John Raymond Wilton, Journal of the London Mathematical Society (1) 20 (1945), 58-64.

  386. G H Hardy and J E Littlewood, Notes on the theory of series (XXIV): A curious power-series, Mathematical Proceedings of the Cambridge Philosophical Society 42 (1946), 85-90.

  387. G H Hardy and W W Rogosinski, Theorems concerning functions subharmonic in a strip, Proceedings of the Royal Society (A) 185 (1946), 1-14.

  388. G H Hardy and W W Rogosinski, Notes on Fourier series (IV): Summability (R2)(R_2), Mathematical Proceedings of the Cambridge Philosophical Society 43 (1947), 10-25.

  389. G H Hardy, A double integral, Journal of the London Mathematical Society (1) 22 (4) (1947), 242-247.

  390. G H Hardy and J E Littlewood, A new proof of a theorem on rearrangements, Journal of the London Mathematical Society (1) 23 (3) (1948), 163-168.

  391. G H Hardy and W W Rogosinski, Notes on Fourier series (V): Summability (R1)(R_1), Mathematical Proceedings of the Cambridge Philosophical Society 45 (1949), 173-185.

Last Updated July 2020