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

Yuichi Hirano

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arXiv · 1707.01314

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

Yuichi Hirano

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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.

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Yuichi Hirano. 2017-07-05. Congruences between Hilbert modular forms of weight $2$, and special values of their $L$-functions. https://arxiv.org/abs/1707.01314

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