Geodesic
Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus 2
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 19-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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Symmetric squares of zeta-functions are introduced for modular forms for the principal congruence subgroup of the integral symplectic group of genus 2. A connection is established between the symmetric squares and Dirichlet series constructed from the Fourier coefficients of modular forms, and an integral representation is obtained. Bibliography: 9 titles. 
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V. A. Gritsenko. Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus 2. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 19-36. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/

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[5] H. Maas, Siegel's modular forms and Dirichlet series, Lect. Notes in Math., 216, 1971 | Zbl

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[7] G. Shimura, “On the holomorphy of certain Dirichlet series”, Proc. London Math. Soc., 31:1 (1975), 79–98 | DOI | MR | Zbl

[8] G. Shimura, “On modular correspondences for $Sp(n, \mathbf{Z})$ and their congruence relations”, Proc. Nat. Acad. Sci. USA, 49:6 (1963), 824–828 | DOI | MR | Zbl

[9] A. Ogg, Modular forms and Dirichlet series, Benjamin, New York, 1969 | MR | Zbl