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.
Table of Contents:
- 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; χ), pg. 43
- §6. AN ALTERNATE METHOD, pg. 66
- §7. SOME APPLICATIONS, pg. 88
- APPENDIX, pg. 100
- BIBLIOGRAPHY, pg. 105