On the analytic properties of standard zeta functions of siegel modular forms

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.