Congruences between Hilbert modular forms of weight $2$, and special values of their $L$-functions

Abstract

The purpose of this paper is to show how a congruence between (the Fourier coefficients of) a Hilbert cusp form and a Hilbert Eisenstein series of parallel weight $2$ gives rise to congruences between algebraic parts of critical values of their $L$-functions. This is a generalization of a result of V. Vatsal.

43 pages

References in corpus (3)

• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Constant terms of Eisenstein series over a totally real field
• Images of Real Representations of $S{L}_n(Z_p)$