Geodesic
Analytic continuation of symmetric squares
Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 593-614

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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. 
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     author = {V. A. Gritsenko},
     title = {Analytic continuation of symmetric squares},
     journal = {Sbornik. Mathematics},
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     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_5_a0/}
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V. A. Gritsenko. Analytic continuation of symmetric squares. Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 593-614. http://geodesic.mathdoc.fr/item/SM_1979_35_5_a0/