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

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