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

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.