# Sarvadaman Chowla

### Quick Info

London, England

Laramie, Wyoming, USA

**Sarvadaman Chowla**was a British-born Indian American mathematician, specializing in number theory.

### Biography

**Sarvadaman Chowla**'s father, Gopal Chowla, was professor of mathematics at Lahore. Gopal Chowla visited England with his wife Shankuntala so that he could study at Cambridge University. It was during the visit to England that Sarvadaman Chowla was born. The family returned to India shortly after his birth and he was brought up there.

At the age of 21 Chowla was awarded his master's degree from Government College in Lahore. He then decided to go to England to study for his doctorate and he undertook research at the University of Cambridge under J E Littlewood's supervision, being awarded his doctorate in 1931. After returning to India, Chowla was appointed professor of mathematics at St Stephen's College in Delhi, then at Benares Hindu University in Benares, then at Andhra University in Waltair, and finally at Government College of Punjab University in Lahore where he was Head of the Department of Mathematics from 1936 to 1947.

This period while Chowla was Head of Mathematics at Lahore was a very difficult one. India was British but Britain wanted to transfer power to a single Indian administration, creating one new country. There were severe divisions in India, however, and in 1946 there was a civil war with rioting and killing throughout the whole of the subcontinent. The Punjab, where Chowla worked, was in one of the most difficult positions being a Muslim majority province with a large Sikh community that had become anti-Muslim. The British Parliament passed the Indian Independence Act in July 1947 which created two independent nations, India and Pakistan, at midnight on 14-15 August 1947.

Chowla was in Lahore which the Indian Independence Act put in Pakistan, close to the new border with India. He fled with his family to Delhi and from there they continued their flight to the United States. There Chowla became a visitor at the Institute for Advanced Study in Princeton, where he remained until the autum of 1949 when he was appointed as professor at the University of Kansas at Lawrence.

After three years at the University of Kansas, Chowla moved to the University of Colorado at Boulder where he remained until 1963. In that year he was offered the post of research professor at the Pennsylvania State University and he was to hold this post until he retired in 1976.

Chowla produced a remarkably rich research output, and his results in many of areas of number theory and combinatorics are of the greatest significance. The range of his work is described in [4]:-

Chowla's first paper appeared in 1925 and his last in 1986. During this period of sixty-two years he wrote about 350 papers. His papers encompassed a wide variety of interests. He wrote on additive number theory (lattice points, partitions, Waring's problem), analysis, Bernoulli numbers, class invariants, definite integrals, elliptic integrals, infinite series, the Weierstrass approximation theorem), analytic number theory (Dirichlet L-functions, primes, Riemann and Epstein zeta functions), binary quadratic forms and class numbers, combinatorial problems (block designs, difference sets, Latin squares), Diophantine equations and Diophantine approximation, elementary number theory (arithmetic functions, continued fractions, and Ramanujan's tau function), and exponential and character sums (Gauss sums, Kloosterman sums, trigonometric sums).He collaborated with a large collection of other mathematicians and many of his papers are written jointly with them. For example around 40 are named in [2], including T M Apostol, E Artin, R Brauer, H Davenport, P Erdős, Marshall Hall, H Hasse, I N Herstein, L J Mordell, S S Pillai, C R Rao, A Selberg, G Shimura, T Skolem, J Todd, A Walfisz and H Zassenhaus.

Among the theorems to which Chowla's name have been attached are the Bruck-Chowla-Ryser theorem on designs (1950); the Ankeny-Artin-Chowla theorem on the class number of real quadratic number fields (1952); the Chowla-Mordell theorem on Gauss sums (1962); and the Chowla-Selberg formula for the product of certain values of the Dedekind eta function.

Among a long list of other results we mention just a very few such as his generalisation of Wolstenholme's theorem; his work on classes of quintics not soluble by radicals; his closed form for the Bernoulli numbers; and his work on the length of the period of the continued fraction expansion of $√N$.

Chowla is described in [4] as a:-

... lively, friendly, and good humored person who was extremely modest about his accomplishments. He was engaged in mathematics to such an extent that he had few outside interests.His teaching is also described:-

Chowla's lectures were both interesting and inspiring. He introduced students to the main ideas of the subject by means of illuminating examples and by giving proofs of important special cases of more general theorems.Among the many honours given to Chowla were the Padmabhushan Award from the Indian National Academy of Sciences, to which he had been elected a member; and an honorary membership of the Royal Norwegian Society of Sciences and Letters.

### References (show)

- J G Huard and K S Williams (eds),
*The Collected Papers of Sarvadaman Chowla, Volumes I-III*, (Montréal, 1999). - R G Ayoub, Sarvadaman Chowla,
*J. Number Theory***11**(3) (1979) 286-301. - R G Ayoub, Erratum : Sarvadaman Chowla,
*J. Number Theory***12**(1) (1980), 139. - R G Ayoub, J G Huard and K S Williams, Sarvadaman Chowla (1907-1995),
*Notices Amer. Math. Soc.***45**(5) (1998), 594-598. http://www.ams.org/notices/199805/comm-chowla.pdf

### Additional Resources (show)

Other websites about Sarvadaman Chowla:

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Written by J J O'Connor and E F Robertson

Last Update October 1998

Last Update October 1998