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 
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/
@article{SM_1977_33_1_a1,
     author = {V. A. Gritsenko},
     title = {Symmetric squares of zeta-functions for the principal congruence subgroup of the {Siegel} group of genus~2},
     journal = {Sbornik. Mathematics},
     pages = {19--36},
     year = {1977},
     volume = {33},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/}
}
TY  - JOUR
AU  - V. A. Gritsenko
TI  - Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus 2
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 19
EP  - 36
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/
LA  - en
ID  - SM_1977_33_1_a1
ER  - 
%0 Journal Article
%A V. A. Gritsenko
%T Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus 2
%J Sbornik. Mathematics
%D 1977
%P 19-36
%V 33
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/
%G en
%F SM_1977_33_1_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] A. N. Andrianov, “Simmetricheskie kvadraty dzeta-funktsii zigelevykh modulyarnykh form roda 2”, Trudy Matem. in-ta im. V. A. Steklova, CXLII (1976), 22–45 | MR

[2] A. N. Andrianov, “Eilerovy proizvedeniya, otvechayuschie modulyarnym formam Zigelya roda 2”, Uspekhi matem. nauk, XXIX:3 (177) (1974), 43–110 | MR

[3] S. A. Evdokimov, “Eilerovy proizvedeniya dlya kongruents-podgrupp zigelevoi gruppy roda 2”, Matem. sb., 99 (141) (1976), 483–514 | MR

[4] A. N. Andrianov, G. N. Maloletkin, “Povedenie teta-ryadov roda $n$ pri modulyarnykh podstanovkakh”, Izv. AN SSSR, seriya matem., 39 (1975), 243–258 | MR | Zbl

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

[6] H. Maas, “Dirichletsche Reihen und Modulformen zweiten Grades”, Acta Arithmetica, 24 (1973), 225–238 | MR | Zbl

[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