Cambridge Journal of Mathematics, v.3, no.3, pp.355 - 438
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.