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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Central values of the symmetric square $L$-functions
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by Wenzhi Luo PDF
Proc. Amer. Math. Soc. 140 (2012), 3313-3322 Request permission

Abstract:

We establish a sharp bound for the square mean of the central values of the symmetric square $L$-functions associated to holomorphic cusp forms of level $1$, as the weight $k$ varies in the short interval $[K,\; K + K^{1/2 + \epsilon }]$.
References
  • Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066
  • I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York-London, 1965. Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin; Translated from the Russian by Scripta Technica, Inc; Translation edited by Alan Jeffrey. MR 0197789
  • H. Iwaniec and P. Michel, The second moment of the symmetric square $L$-functions, Ann. Acad. Sci. Fenn. Math. 26 (2001), no. 2, 465–482. MR 1833252
  • M. Jutila, On the mean value of $L({1\over 2},\,\chi )$ for real characters, Analysis 1 (1981), no. 2, 149–161. MR 632705, DOI 10.1524/anly.1981.1.2.149
  • Rizwanur Khan, Non-vanishing of the symmetric square $L$-function at the central point, Proc. Lond. Math. Soc. (3) 100 (2010), no. 3, 736–762. MR 2640289, DOI 10.1112/plms/pdp048
  • Winfried Kohnen and Jyoti Sengupta, On the average of central values of symmetric square $L$-functions in weight aspect, Nagoya Math. J. 167 (2002), 95–100. MR 1924720, DOI 10.1017/S0027763000025447
  • Goro Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), no. 1, 79–98. MR 382176, DOI 10.1112/plms/s3-31.1.79
  • D. Zagier, Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977, pp. 105–169. MR 0485703
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Additional Information
  • Wenzhi Luo
  • Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
  • MR Author ID: 260185
  • Email: wluo@math.ohio-state.edu
  • Received by editor(s): February 10, 2011
  • Received by editor(s) in revised form: March 31, 2011
  • Published electronically: January 31, 2012
  • Additional Notes: The author’s research was partially supported by NSF grant DMS-0855600
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 3313-3322
  • MSC (2010): Primary 11F11, 11F66, 11F67
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11174-8
  • MathSciNet review: 2929002