Kenkichi Iwasawa Knihy

The notes provide a comprehensive account of the adelic approach to Hecke's L-functions related to number fields, detailing analytic continuation, functional equations, and the class number formula from the Dedekind zeta function. This approach, independently discovered by Iwasawa and Tate, laid the groundwork for modern studies in automorphic forms and L-series. The volume fills a significant gap in the literature, as Iwasawa's insights had not been previously published in detail, culminating in an elegant explanation of classical results regarding prime ideals and cyclotomic fields.

Kenkichi Iwasawa is one of the most original and influential mathematicians in the 20-th century. He made a number of fundamental contributions in group theory and algebraic number theory. In group theory, he created the theory of (L)-groups (including the structure theorem called "Iwasawa decomposition"), which played an important role in the solution of Hilbert's Fifth Problem. In number theory, he constructed a beautiful theory on Z-extentions, now called "Iwasawa theory," realizing the deep analogy between number fields and algebraic function fields. Iwasawa theory gave a strong influence to the recent development of arithmetic algebraic geometry (including the solution of Fermat's Last Theorem). This Collected Papers of K. Iwasawa contains all 66 published papers, including 11 papers in Japanese, for which English abstracts (by the editors) are attached. These volumes include 5 (newly found) unpublished papers. They also include a masterly summery of Iwasawa theory by J. Coates (Cambridge Univ.).