Lectures on P-Adic L-Functions. (AM-74), Volume 74

Kinkichi Iwasawa

Published by Princeton University Press 1972

Lectures on P-Adic L-Functions. (AM-74), Volume 74

Kinkichi Iwasawa

Volume 74 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400881703

Overview
Contents

About this book

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.

Topics

Frontmatter Publicly Available Download PDF	i
PREFACE Kenkichi Iwasawa Requires Authentication Unlicensed Licensed Download PDF	v
CONTENTS Publicly Available Download PDF	vii
§1. DIRICHLET’S L-FUNCTIONS Requires Authentication Unlicensed Licensed Download PDF	1
§2. GENERALIZED BERNOULLI NUMBERS Requires Authentication Unlicensed Licensed Download PDF	7
§3. p-ADIC L-FUNCTIONS Requires Authentication Unlicensed Licensed Download PDF	17
§4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS Requires Authentication Unlicensed Licensed Download PDF	36
§5. CALCULATION OF L_p (1; χ) Requires Authentication Unlicensed Licensed Download PDF	43
§6. AN ALTERNATE METHOD Requires Authentication Unlicensed Licensed Download PDF	66
§7. SOME APPLICATIONS Requires Authentication Unlicensed Licensed Download PDF	88
APPENDIX Requires Authentication Unlicensed Licensed Download PDF	100
BIBLIOGRAPHY Requires Authentication Unlicensed Licensed Download PDF	105