Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa.
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...
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Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1972 |
Year of Publication: | 2016 |
Language: | English |
Series: | Annals of Mathematics Studies ;
74 |
Online Access: | |
Physical Description: | 1 online resource (112 p.) |
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Other title: | 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; χ) -- §6. AN ALTERNATE METHOD -- §7. SOME APPLICATIONS -- APPENDIX -- BIBLIOGRAPHY |
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Summary: | 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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9781400881703 9783110494914 9783110442496 |
DOI: | 10.1515/9781400881703 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Kinkichi Iwasawa. |