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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 302, Pages 149–167 (Mi znsl927)  

This article is cited in 4 scientific papers (total in 4 papers)

Behavior of automorphic $l$-functions at the points $s=1$ and $s=1/2$

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (255 kB) Citations (4)
References:
Abstract: Let $S_k(N)^+$ be the set of primitive cusp forms of even weight $k$ for $\Gamma_0(N)$ and let $L(s,\operatorname{sym}^2f)$ be the symmetric square $L$-function $L(s,f)$ of a form $f\in S_k(N)^+$. The moments of the variable $L(s,\operatorname{sym}^2f)$, $f\in S_2(N)^+$, are computed for $N=p$, and the corresponding limiting distribution is determined in $N$-aspect. Let $f\in S_k(1)^+$, $g\in S_l(1)^+$, and $\omega_f=\Gamma(k-1)/(4\pi)^{k-1}{\langle f,f\rangle}$. Asymptotic formulas for $\sum_{f\in S_k(1)^+}\omega_f L\Bigl(\frac12,\operatorname{sym}^2 f\Bigr)$ and $\sum_{f\in S_k(1)^+}\omega_f L\Bigl(\frac12,f\otimes g\Bigr)$ as $k\in\infty$ are obtained.
Received: 19.09.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 129, Issue 3, Pages 3898–3909
DOI: https://doi.org/10.1007/s10958-005-0326-5
Bibliographic databases:
UDC: 511.466+517.863
Language: Russian
Citation: O. M. Fomenko, “Behavior of automorphic $l$-functions at the points $s=1$ and $s=1/2$”, Analytical theory of numbers and theory of functions. Part 19, Zap. Nauchn. Sem. POMI, 302, POMI, St. Petersburg, 2003, 149–167; J. Math. Sci. (N. Y.), 129:3 (2005), 3898–3909
Citation in format AMSBIB
\Bibitem{Fom03}
\by O.~M.~Fomenko
\paper Behavior of automorphic $l$-functions at the points $s=1$ and $s=1/2$
\inbook Analytical theory of numbers and theory of functions. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 302
\pages 149--167
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl927}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2023038}
\zmath{https://zbmath.org/?q=an:1140.11332}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 3
\pages 3898--3909
\crossref{https://doi.org/10.1007/s10958-005-0326-5}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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