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

 

Central values of the symmetric square $ L$-functions


Author: Wenzhi Luo
Journal: Proc. Amer. Math. Soc. 140 (2012), 3313-3322
MSC (2010): Primary 11F11, 11F66, 11F67
Published electronically: January 31, 2012
MathSciNet review: 2929002
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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 }]$.


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Additional Information

Wenzhi Luo
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
Email: wluo@math.ohio-state.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11174-8
PII: S 0002-9939(2012)11174-8
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.