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Congruence of Siegel modular forms and special values of their standard zeta functions

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Abstract

In this paper, we consider the relationship between the congruence of cuspidal Hecke eigenforms with respect to Sp n (Z) and the special values of their standard zeta functions. In particular, we propose a conjecture concerning the congruence between Saito-Kurokawa lifts and non-Saito-Kurokawa lifts, and prove it under certain condition.

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Correspondence to Hidenori Katsurada.

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Partially supported by Grant-in-Aid for Scientific Research C-17540003, JSPS.

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Katsurada, H. Congruence of Siegel modular forms and special values of their standard zeta functions. Math. Z. 259, 97–111 (2008). https://doi.org/10.1007/s00209-007-0213-5

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