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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Average values of symmetric square $L$-functions at the edge of the critical strip


Author: J. Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 1063-1070
MSC (2000): Primary 11F67
Published electronically: July 26, 2002
MathSciNet review: 1948096
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Abstract: Let ${\mathcal{B}}_{2}^{*}(N)$ be the set of all normalized newforms of weight 2 and level $N$, and let $L({\operatorname{sym}}^{2}f, 1)$ be the symmetric square $L$-function associated to $f\in {\mathcal{B}}_{2}^{*}(N)$. If $N$ is a prime, then there is a positive constant $B$ such that

\begin{displaymath}\sum _{f\in {\mathcal{B}}_{2}^{*}(N)} L(1,{\operatorname{sym}... ...{\frac{\pi ^{4}}{432}} N + O\big (N^{27/28} (\log N)^{B}\big ).\end{displaymath}

This improves a recent result of Akbary, which requires $45/46$ in place of $27/28$.


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Additional Information

J. Wu
Affiliation: Institut Élie Cartan, UMR 7502 UHP-CNRS-INRIA, Université Henri Poincaré (Nancy 1), 54506 Vandœuvre–lès–Nancy, France
Email: wujie@iecn.u-nancy.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06725-4
PII: S 0002-9939(02)06725-4
Received by editor(s): November 12, 2001
Published electronically: July 26, 2002
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2002 American Mathematical Society