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

 

On the error term in an asymptotic formula for the symmetric square $L$-function


Author: Yuk-Kam Lau
Journal: Proc. Amer. Math. Soc. 132 (2004), 317-323
MSC (2000): Primary 11F67
Published electronically: June 17, 2003
MathSciNet review: 2022351
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Abstract: Recently Wu proved that for all primes $q$,

\begin{displaymath}\sum_{f} L(1, \mbox{sym}^2f) =\frac{\pi^4}{432}q +O(q^{27/28}\log^B q) \end{displaymath}

where $f$ runs over all normalized newforms of weight 2 and level $q$. Here we show that $27/28$ can be replaced by $9/10$.


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Additional Information

Yuk-Kam Lau
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: yklau@maths.hku.hk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07027-8
PII: S 0002-9939(03)07027-8
Received by editor(s): September 17, 2002
Published electronically: June 17, 2003
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2003 American Mathematical Society