Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa
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| Autore: |
Iwasawa Kinkichi
|
| Titolo: |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa
|
| Pubblicazione: | Princeton, NJ : , : Princeton University Press, , [2016] |
| ©1972 | |
| Descrizione fisica: | 1 online resource (116 pages) |
| Disciplina: | 512/.74 |
| Soggetto topico: | L-functions |
| Algebraic number theory | |
| Soggetto non controllato: | Abelian extension |
| Absolute value | |
| Algebraic closure | |
| Algebraic number field | |
| Algebraic number theory | |
| Algebraic number | |
| Algebraically closed field | |
| Arithmetic function | |
| Class field theory | |
| Complex number | |
| Conjecture | |
| Cyclotomic field | |
| Dirichlet character | |
| Existential quantification | |
| Finite group | |
| Integer | |
| L-function | |
| Mellin transform | |
| Meromorphic function | |
| Multiplicative group | |
| P-adic L-function | |
| P-adic number | |
| Power series | |
| Prime number | |
| Quadratic field | |
| Rational number | |
| Real number | |
| Root of unity | |
| Scientific notation | |
| Series (mathematics) | |
| Special case | |
| Subgroup | |
| Theorem | |
| Topology | |
| Classificazione: | SI 830 |
| Persona (resp. second.): | IwasawaKenkichi |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | 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 |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Lectures on P-Adic L-Functions. (AM-74), Volume 74 |
| ISBN: | 1-4008-8170-6 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910154753503321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of mathematics studies ; ; Number 74.