Kenkichi Iwasawa

Iwasawa Kenkichi (Japanese岩 泽 健 吉; born September 11, 1917 in Shinshuku, Kiryu, † October 26, 1998 in Tokyo ) was a Japanese mathematician who made ​​fundamental contributions to algebraic number theory, especially the theory of cyclotomic fields provided. He also dealt with topological groups and Lie groups.

Life

Iwasawa was in Tokyo on the Musashi High School - the forerunner of today's Musashi University -. , And studied at the Imperial University of Tokyo from 1937 1940 he graduated, became an assistant and received his PhD in 1945 During the war years he became ill with pleurisy and was until 1947 on. the University to return, where he was assistant professor 1949-1955. In 1950 he traveled to the United States, where he was an Invited Lecture at ICM 1950 in Cambridge (Massachusetts ) (A note on L functions). From 1950 to 1952 he was at the Institute for Advanced Study in Princeton (New Jersey), then to 1967 professor at MIT in Cambridge (Massachusetts ) and then until his retirement in 1986 Professor at Princeton. In 1987 he returned with his wife to Tokyo.

Work

Iwasawa is mainly known for his work on algebraic number theory, especially the creation of the low-lying Iwasawa theory of extensions of algebraic number fields, in which he, for example, in the theory of cyclotomic fields, not only the body of the p- th roots of unity over the rational numbers ( with p odd prime ) is considered, but at the same time the infinite tower of cyclotomic fields formed by the adjunction of roots of unity.

The starting point was his attempt, the criterion of Ernst Eduard Kummer for the characterization of irregular primes to understand (which divide the class number of the body of the p- th roots of unity over the rational numbers ) and the p- adic zeta functions of Kubota and Leopoldt. On the relation of analytic and algebraic aspects of his theory he put the Iwasawa on assumptions that were later proved by Barry Mazur and Andrew Wiles.

In addition to his work in number theory made ​​him also his work on the theory of topological groups and Lie groups known. He made important works ( Annals of Mathematics 1949) to solve the fifth Hilbert problem ( which asks whether every locally Euclidean topological group is a Lie group), then a very active area of ​​research. In this context, he cited 1949, the Iwasawa decomposition on (On some types of topological groups, Annals of Mathematics ).

In Japan, he received in 1959 the Asahi price, the 1962 price of the Japanese Academy, 1979 Fujiwara price. In 1962 he received the Cole prize. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( On some infinite abelian extensions of algebraic number fields ) and 1962 in Stockholm (A class number formula for cyclotomic fields ).

His students included Ralph Greenberg and Lawrence C. Washington.

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