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A Dirichlet series attached to three Siegel modular forms

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Abstract

For three Siegel modular forms of degrees \(n_1, n_2\) and \(n_1+n_2-1\) respectively, we attach a certain Dirichlet series which has a meromorphic continuation to the whole complex plane and satisfies a functional equation. We also show some algebraicity property of its special values. For the proof we use a Rankin-Selberg type integral involving a pullback of Siegel-Eisenstein series of degree \(2n_1+2n_2-1\). In some special cases our series coincides with known Dirichlet series associated with automorphic L-functions.

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  1. Department of Mathematics, Tokyo Institute of Technology, Oo-okayama, Meguro-ku, Tokyo, 152-8551, Japan

    Shin-ichiro Mizumoto

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  1. Shin-ichiro Mizumoto
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Correspondence to Shin-ichiro Mizumoto.

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Communicated by Jens Funke.

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Mizumoto, Si. A Dirichlet series attached to three Siegel modular forms. Abh. Math. Semin. Univ. Hambg. 87, 113–134 (2017). https://doi.org/10.1007/s12188-016-0139-0

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  • DOI: https://doi.org/10.1007/s12188-016-0139-0

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