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Mathematics of the USSR-Sbornik, 1979, Volume 35, Issue 5, Pages 593–614
DOI: https://doi.org/10.1070/SM1979v035n05ABEH001575
(Mi sm2677)
 

This article is cited in 8 scientific papers (total in 8 papers)

Analytic continuation of symmetric squares

V. A. Gritsenko
References:
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
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1978, Volume 107(149), Number 3(11), Pages 323–346
Bibliographic databases:
UDC: 511.944
MSC: Primary 32N15, 30A58; Secondary 20G30, 10D20, 20H10
Language: English
Original paper language: Russian
Citation: V. A. Gritsenko, “Analytic continuation of symmetric squares”, Mat. Sb. (N.S.), 107(149):3(11) (1978), 323–346; Math. USSR-Sb., 35:5 (1979), 593–614
Citation in format AMSBIB
\Bibitem{Gri78}
\by V.~A.~Gritsenko
\paper Analytic continuation of symmetric squares
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 3(11)
\pages 323--346
\mathnet{http://mi.mathnet.ru/sm2677}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=515736}
\zmath{https://zbmath.org/?q=an:0426.10025|0394.10014}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 5
\pages 593--614
\crossref{https://doi.org/10.1070/SM1979v035n05ABEH001575}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JG48000001}
Linking options:
  • https://www.mathnet.ru/eng/sm2677
  • https://doi.org/10.1070/SM1979v035n05ABEH001575
  • https://www.mathnet.ru/eng/sm/v149/i3/p323
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:289
    Russian version PDF:113
    English version PDF:15
    References:56
    First page:1
     
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