書誌事項

Lectures on p-adic L-functions

by Kenkichi Iwasawa

(Annals of mathematics studies, no. 74)

Princeton University Press, 1972

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注記

Bibliography: p. 105-106

内容説明・目次

内容説明

An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.

目次

  • *Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii* 1. DIRICHLET'S L-FUNCTIONS, pg. 1* 2. GENERALIZED BERNOULLI NUMBERS, pg. 7* 3. p-ADIC L-FUNCTIONS, pg. 17* 4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS, pg. 36* 5. CALCULATION OF Lp (1
  • chi), pg. 43* 6. AN ALTERNATE METHOD, pg. 66* 7. SOME APPLICATIONS, pg. 88*APPENDIX, pg. 100*BIBLIOGRAPHY, pg. 105

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