On the transfer congruence between p-adic Hecke L-functions

2014/11/05 by Dohyeong Kim, Kim, Dohyeong
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1411.1184

59 pages

arxiv created 2014/11/05 · openalex publication_date 2014/11/05 · arxiv updated 2014/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the transfer congruence between p-adic Hecke L-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer's congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the q-expansion principle, and some modification of Hsieh's Whittaker model for Katz' Eisenstein series. As a first application, we prove explicit congruence between special values of Hasse-Weil L-function of a CM elliptic curve twisted by Artin representations. As a second application, we prove the existence of a non-commutative p-adic L-function in the algebraic K₁-group of the completed localized Iwasawa algebra.

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