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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1978 Volume 107(149), Number 3(11), Pages 323–346 (Mi sm2677)

This article is cited 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.

UDC: 511.944

MSC: Primary 32N15, 30A58; Secondary 20G30, 10D20, 20H10

Received: 05.04.1978


 English version:
Mathematics of the USSR-Sbornik, 1979, 35:5, 593–614

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