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- P-adic_L-function abstract "In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic (where p is a prime number). For example, the domain could be the p-adic integers Zp, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbers Qp or its algebraic closure.The source of a p-adic L-function tends to be one of two types. The first source—from which Tomio Kubota and Heinrich-Wolfgang Leopoldt gave the first construction of a p-adic L-function (Kubota & Leopoldt 1964)—is via the p-adic interpolation of special values of L-functions. For example, Kubota–Leopoldt used Kummer's congruences for Bernoulli numbers to construct a p-adic L-function, the p-adic Riemann zeta function ζp(s), whose values at negative odd integers are those of the Riemann zeta function at negative odd integers (up to an explicit correction factor). p-adic L-functions arising in this fashion are typically referred to as analytic p-adic L-functions. The other major source of p-adic L-functions—first discovered by Kenkichi Iwasawa—is from the arithmetic of cyclotomic fields, or more generally, certain Galois modules over towers of cyclotomic fields or even more general towers. A p-adic L-function arising in this way is typically called an arithmetic p-adic L-function as it encodes arithmetic data of the Galois module involved. The main conjecture of Iwasawa theory (now a theorem due to Barry Mazur and Andrew Wiles) is the statement that the Kubota–Leopoldt p-adic L-function and an arithmetic analogue constructed by Iwasawa theory are essentially the same. In more general situations where both analytic and arithmetic p-adic L-functions are constructed (or expected), the statement that they agree is called the main conjecture of Iwasawa theory for that situation. Such conjectures represent formal statements concerning the philosophy that special values of L-functions contain arithmetic information.".
- P-adic_L-function wikiPageExternalLink ?GDZPPN002180626.
- P-adic_L-function wikiPageExternalLink tsinghua.pdf.
- P-adic_L-function wikiPageExternalLink item?id=GAU_1977-1978__5__A9_0.
- P-adic_L-function wikiPageExternalLink item?id=SB_1988-1989__31__33_0.
- P-adic_L-function wikiPageID "22059815".
- P-adic_L-function wikiPageLength "8657".
- P-adic_L-function wikiPageOutDegree "39".
- P-adic_L-function wikiPageRevisionID "610612350".
- P-adic_L-function wikiPageWikiLink Algebraic_closure.
- P-adic_L-function wikiPageWikiLink American_Mathematical_Society.
- P-adic_L-function wikiPageWikiLink Andrew_Wiles.
- P-adic_L-function wikiPageWikiLink Annals_of_Mathematics.
- P-adic_L-function wikiPageWikiLink Barry_Mazur.
- P-adic_L-function wikiPageWikiLink Bernoulli_number.
- P-adic_L-function wikiPageWikiLink Category:Zeta_and_L-functions.
- P-adic_L-function wikiPageWikiLink Class_field_theory.
- P-adic_L-function wikiPageWikiLink Codomain.
- P-adic_L-function wikiPageWikiLink Crelles_Journal.
- P-adic_L-function wikiPageWikiLink Cyclotomic_field.
- P-adic_L-function wikiPageWikiLink Domain_of_a_function.
- P-adic_L-function wikiPageWikiLink Galois_module.
- P-adic_L-function wikiPageWikiLink Galois_representation.
- P-adic_L-function wikiPageWikiLink Generalized_Bernoulli_number.
- P-adic_L-function wikiPageWikiLink Heinrich-Wolfgang_Leopoldt.
- P-adic_L-function wikiPageWikiLink Inventiones_Mathematicae.
- P-adic_L-function wikiPageWikiLink Journal_für_die_reine_und_angewandte_Mathematik.
- P-adic_L-function wikiPageWikiLink Kenkichi_Iwasawa.
- P-adic_L-function wikiPageWikiLink Kummer_congruence.
- P-adic_L-function wikiPageWikiLink Kummers_congruence.
- P-adic_L-function wikiPageWikiLink L-function.
- P-adic_L-function wikiPageWikiLink Main_conjecture_of_Iwasawa_theory.
- P-adic_L-function wikiPageWikiLink Mathematics.
- P-adic_L-function wikiPageWikiLink Mazur–Mellin_transform.
- P-adic_L-function wikiPageWikiLink P-adic_distribution.
- P-adic_L-function wikiPageWikiLink P-adic_integer.
- P-adic_L-function wikiPageWikiLink P-adic_measure.
- P-adic_L-function wikiPageWikiLink P-adic_number.
- P-adic_L-function wikiPageWikiLink Prime_number.
- P-adic_L-function wikiPageWikiLink Princeton_University_Press.
- P-adic_L-function wikiPageWikiLink Profinite_group.
- P-adic_L-function wikiPageWikiLink Riemann_zeta_function.
- P-adic_L-function wikiPageWikiLink Special_values_of_L-functions.
- P-adic_L-function wikiPageWikiLink Springer-Verlag.
- P-adic_L-function wikiPageWikiLink Springer_Science+Business_Media.
- P-adic_L-function wikiPageWikiLink Teichmüller_character.
- P-adic_L-function wikiPageWikiLink Tomio_Kubota.
- P-adic_L-function wikiPageWikiLink Tower_of_fields.
- P-adic_L-function wikiPageWikiLinkText "''p''-Adic L-functions".
- P-adic_L-function wikiPageWikiLinkText "''p''-adic ''L''-function".
- P-adic_L-function wikiPageWikiLinkText "''p''-adic ''L''-functions".
- P-adic_L-function wikiPageWikiLinkText "''p''-adic Dirichlet ''L''-function".
- P-adic_L-function wikiPageWikiLinkText "''p''-adic L-functions".
- P-adic_L-function wikiPageWikiLinkText "p-adic L-function".
- P-adic_L-function hasPhotoCollection P-adic_L-function.
- P-adic_L-function wikiPageUsesTemplate Template:Citation.
- P-adic_L-function wikiPageUsesTemplate Template:Harv.
- P-adic_L-function wikiPageUsesTemplate Template:Harvtxt.
- P-adic_L-function subject Category:Zeta_and_L-functions.
- P-adic_L-function hypernym Function.
- P-adic_L-function type ProgrammingLanguage.
- P-adic_L-function type Function.
- P-adic_L-function comment "In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic (where p is a prime number). For example, the domain could be the p-adic integers Zp, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbers Qp or its algebraic closure.The source of a p-adic L-function tends to be one of two types.".
- P-adic_L-function label "P-adic L-function".
- P-adic_L-function sameAs Función_L_p-ádica.
- P-adic_L-function sameAs P-進L-函数.
- P-adic_L-function sameAs m.05p8cfm.
- P-adic_L-function sameAs Q7116913.
- P-adic_L-function sameAs Q7116913.
- P-adic_L-function wasDerivedFrom P-adic_L-function?oldid=610612350.
- P-adic_L-function isPrimaryTopicOf P-adic_L-function.