Geodesic
On the analytic properties of standard zeta functions of siegel modular forms
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that standard zeta functions (analogs of the zeta functions of Rankin and Shimura) for holomorphic cusp forms with respect to congruence subgroups of the form $$ \Gamma_0^n(q)=\biggl\{\begin{pmatrix}A&B\\C&D\end{pmatrix}\in Sp_n(\mathbf Z);\quad C\equiv0\pmod q\biggr\} $$ of the Siegel modular group $Sp_n(\mathbf Z)$ of arbitrary even degree $n$ have a meromorphic continuation. For the case $q=1$, with some additional restrictions, it is proved that the zeta functions are holomorphic except for a finite number of poles, and a functional equation is obtained. Bibliography: 9 titles. 
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A. N. Andrianov; V. L. Kalinin. On the analytic properties of standard zeta functions of siegel modular forms. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a0/

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