04044nam 22009855 450 991015475350332120190708092533.01-4008-8170-610.1515/9781400881703(CKB)3710000000620071(SSID)ssj0001651296(PQKBManifestationID)16426393(PQKBTitleCode)TC0001651296(PQKBWorkID)14003656(PQKB)10471831(MiAaPQ)EBC4738558(DE-B1597)467952(OCoLC)979579082(DE-B1597)9781400881703(EXLCZ)99371000000062007120190708d2016 fg engurcnu||||||||txtccrLectures on P-Adic L-Functions. (AM-74), Volume 74 /Kinkichi IwasawaPrinceton, NJ : Princeton University Press, [2016]©19721 online resource (116 pages)Annals of Mathematics Studies ;271Bibliographic Level Mode of Issuance: Monograph0-691-08112-3 Includes bibliographical references.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 -- BIBLIOGRAPHYAn 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.Annals of mathematics studies ;Number 74.L-functionsAlgebraic number theoryAbelian 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.L-functions.Algebraic number theory.512/.74SI 830rvkIwasawa Kinkichi, 1207597Iwasawa Kenkichi, ctbhttps://id.loc.gov/vocabulary/relators/ctbDE-B1597DE-B1597BOOK9910154753503321Lectures on P-Adic L-Functions. (AM-74), Volume 742785744UNINA