Kim, Dohyeong On the transfer congruence between \(p\)-adic Hecke \(L\)-functions. (English) Zbl 1333.11111 Camb. J. Math. 3, No. 3, 355-438 (2015). Author’s 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 \(K_1\)-group of the completed localized Iwasawa algebra. Reviewer: Andrzej Dąbrowski (Szczecin) Cited in 1 Document MSC: 11S40 Zeta functions and \(L\)-functions 11R23 Iwasawa theory 11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces Keywords:Hilbert modular forms; \(p\)-adic \(L\)-functions; Katz’ \(p\)-adic modular forms; Iwasawa main conjecture; false Tate curve extensions PDFBibTeX XMLCite \textit{D. Kim}, Camb. J. Math. 3, No. 3, 355--438 (2015; Zbl 1333.11111) Full Text: DOI arXiv