Lectures on P-Adic L-Functions
1st Edition
Published on 20. June 2016
112 pages
978-1-4008-8170-3 (ISBN)
Description
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.
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.
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Kenkichi Iwasawa
Lectures on P-Adic L-Functions
Book
07/1972
Princeton University Press
€54.40
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Person
Kinkichi Iwasawa
Content
- Frontmatter,
- PREFACE,
- CONTENTS,
- §1. DIRICHLET'S L-FUNCTIONS,
- §2. GENERALIZED BERNOULLI NUMBERS,
- §3. p-ADIC L-FUNCTIONS,
- §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS,
- §5. CALCULATION OF Lp (1; ¿),
- §6. AN ALTERNATE METHOD,
- §7. SOME APPLICATIONS,
- APPENDIX,
- BIBLIOGRAPHY,
