Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa

• Autore: Iwasawa Kinkichi
• 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
• Serie: Annals of mathematics studies ; ; Number 74.