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Algebra i Analiz, 2007, Volume 19, Issue 5, Pages 246–264 (Mi aa143)  
This article is cited in 14 scientific papers (total in 14 papers)

Research Papers

Mean value theorems for automorphic $L$-functions

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (206 kB) Citations (14)
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Abstract: Let $f$ be a holomorphic Hecke eigencuspform of even weight $k\ge 12$ for $\mathrm{SL}(2, \mathbb{Z})$ and let $L(s,\mathrm{sym}^2f)$ be the symmetric square $L$-function of $f$. Let $C(x)$ be the summatory function of the coefficients of $L(s,\mathrm{sym}^2 f)$. The true order is found for
$$ \int_0^x C(y)^2\,dy. $$
Keywords: Symmetric square $L$-function, summatory function, Euler product, Voronoi formula, mean value.
Received: 05.04.2007
English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 5, Pages 853–866
DOI: https://doi.org/10.1090/S1061-0022-08-01024-8
Bibliographic databases:
Document Type: Article
MSC: 11M41
Language: Russian
Citation: O. M. Fomenko, “Mean value theorems for automorphic $L$-functions”, Algebra i Analiz, 19:5 (2007), 246–264; St. Petersburg Math. J., 19:5 (2008), 853–866
Citation in format AMSBIB
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\by O.~M.~Fomenko
\paper Mean value theorems for automorphic $L$-functions
\jour Algebra i Analiz
\yr 2007
\vol 19
\issue 5
\pages 246--264
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\zmath{https://zbmath.org/?q=an:1206.11061}
\transl
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 5
\pages 853--866
\crossref{https://doi.org/10.1090/S1061-0022-08-01024-8}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267421000010}
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:451
    Full-text PDF :99
    References:58
    First page:7
     
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