|
This article is cited in 8 scientific papers (total in 8 papers)
Analytic continuation of symmetric squares
V. A. Gritsenko
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.
Received: 05.04.1978
Citation:
V. A. Gritsenko, “Analytic continuation of symmetric squares”, Math. USSR-Sb., 35:5 (1979), 593–614
Linking options:
https://www.mathnet.ru/eng/sm2677https://doi.org/10.1070/SM1979v035n05ABEH001575 https://www.mathnet.ru/eng/sm/v149/i3/p323
|
|