# Zyoiti Suetuna

### Born: November 1898 in Kunisaki, South Island, Japan

Died: August 1970 in Tokyo, Japan

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After being educated in his home town,

**Zyoiti Suetuna**moved to Tokyo in 1916 when he began to study at the First High School. Certainly his talents had been recognised at his local school for the First High School was only designed for the most talented pupils to finish their school education before entering university. At the First High School Suetuna's mathematical talents became clear to his teachers and in 1919 he entered Tokyo University to take a degree in mathematics.

This was an exciting period to study at Tokyo University for Takagi published his famous paper on class field theory in 1920. When Suetuna was in his final undergraduate year his studies were supervised by Takagi and this inspired Suetuna to work on number theory. He graduated from Tokyo University in 1922 and was appointed as a lecturer at Kyushu University. While he was there he read Edmund Landau's two volume work on the distribution of the primes and then began to read the papers of Hardy and Littlewood which were being published at that time. In particular he read Hardy and Littlewood's paper

*The approximate functional equation in the theory of the zeta function with applications to the divisor problems of Dirichlet and Piltz*which appeared in the

*Proceedings of the London Mathematical Society*. This paper formed the basis for the first sixteen of Suetuna's papers which were on

*L*-functions (generalisations of the zeta function) and appeared from 1924 up to 1931.

Suetuna taught for two years at Kyushu University, being promoted to associate professor during that period, then returned to Tokyo University in 1924. In 1927 Suetuna went to study in Europe, in particular spending two years at Göttingen with Landau's school. While there he became particularly interested in the work on the foundations of mathematics which was being studied by Hilbert's school. He attended lectures by Bernays on the foundations of mathematics during his stay in Göttingen. Another active research group in Göttingen at this time was the algebra group led by Emmy Noether. The style of mathematical research carried out by this group with its lively discussion seminars impressed Suetuna so much that he went on to introduce this research style to Japan on his return.

Now 1927, the year Suetuna went to Europe, was the one in which Artin published his general reciprocity law which in some sense completed the proofs of the ideas Takagi had introduced in 1920. Suetuna was fascinated by this result of Artin and he went to Hamburg in 1929 to study with him. Hasse was also proving important results in this area and Suetuna collaborated with Hasse visiting him in Halle in 1929 to complete work on their joint paper

*A general divisor problem*.

The European trip had been extremely productive for Suetuna and when he returned to Tokyo University in 1931 he had gained greatly from the experience. One purpose of his visit had been to learn probability and statistics, for these topics did not have active researchers in Japan at this time and Tokyo University had sent him to Germany to gain expertise in these areas. Suetuna did not spent a great deal of time attending lectures on probability and statistics, preferring to work on his own research topics. However he did read books on probability and statistics while in Germany and by the time he returned to Japan he had gained considerable expertise in probability and statistics despite concentrating on his research topics in algebra and number theory.

Back in Japan Suetuna introduced a weekly seminar on the Göttingen style where new research results could be discussed. He continued to publish research papers on topics related to Artin's 1927 paper and he also wrote several books: one on algebra and number theory, one on analytic number theory, and one on probability. All were based on lecture courses he gave, the probability book being based on a ten lecture course he was invited to give at Hokkaidu University in 1940. The

*Analytical theory of numbers*was originally published in the form of lecture notes but in 1950 a revised edition was published which incorporated recent developments of the theory. Ikehara, reviewing the book , writes:-

Suetuna was appointed to Takagi's chair in 1936 when Takagi retired; Suetuna had been promoted to full professor in the previous year. The Second World War disrupted life in Japan and in particular it essentially ended Suetuna's research career. After the War he published some articles on the foundations of mathematics and mathematical philosophy which were areas of interest for him. He was particularly interested in Buddhism and this strongly influenced his philosophical thinking. The paper [2] details his publications consisting of thirty works on number theory, twelve on the foundations of mathematics and eight on Buddhist philosophy. These eight publications make Suetuna an important figure in Buddhist philosophy and probably mean that he is more famous for that topic than he is for mathematics.This book, based mainly on the Riemann zeta-functions and L-functions, is a unique exposition of the analytical theory of numbers in a modern sense as can be seen from the chapter headings: I)Riemann's zeta-functions; II)Hecke's L-functions; III)Dirichlet's L-functions; and IV)Artin's L-series.

Suetuna was elected to the Japan Academy in 1947. he retired from his chair in Tokyo University in 1959 and was appointed as Director of the Institute of Statistical Mathematics.

**Article by:** *J J O'Connor* and *E F Robertson*

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