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Record Nr. |
UNINA9910154753503321 |
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Autore |
Iwasawa Kinkichi |
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Titolo |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1972 |
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ISBN |
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Descrizione fisica |
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1 online resource (116 pages) |
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Collana |
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Annals of Mathematics Studies ; ; 271 |
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Classificazione |
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Disciplina |
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Soggetti |
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L-functions |
Algebraic number theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Frontmatter -- PREFACE / Iwasawa, Kenkichi -- 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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Sommario/riassunto |
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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. |
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