Abstract:
In this paper the author constructs a holomorphic analytic continuation onto the whole complex plane of special Euler products-symmetric squares-corresponding to Siegel modular forms for congruence-subgroups of $\operatorname{Sp}_2(\mathbf Z)$.
The proof of this theorem is based on the analytic properties of “mixed” Eisenstein series for “arithmetic” congruence-subgroups $\Gamma_0(q)$ of $\operatorname{Sp}_2(\mathbf Z)$ with character $\chi$. The paper contains a proof that holomorphic analytic continuation onto the whole complex plane is possible for these series, and a derivation of their functional equation in the case of primitive $\chi$.
Bibliography: 13 titles.