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

2017/07/05 by Hirano, Yuichi
#11F30 #11F33 #11F41 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1707.01314

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.

Related

• Notes on the arithmetic of Hilbert modular forms
• Determining Hilbert Modular Forms by Central Values of Rankin-Selberg Convolutions: The Weight Aspect
• Canonical periods and congruence formulae
• Characterizing Hilbert modular cusp forms by coefficient size
• Hilbert modular Eisenstein congruences of local origin