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 | References | Similar Articles | Additional Information

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 $9/10$.

References [Enhancements On Off] (What's this?)

  • 1. Amir Akbary, Average values of symmetric square 𝐿-functions at 𝑅𝑒(𝑠)=2, C. R. Math. Acad. Sci. Soc. R. Can. 22 (2000), no. 3, 97–104 (English, with French summary). MR 1777313
  • 2. Aleksandar Ivić, The Riemann zeta-function, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1985. The theory of the Riemann zeta-function with applications. MR 792089
  • 3. Henryk Iwaniec, Wenzhi Luo, and Peter Sarnak, Low lying zeros of families of 𝐿-functions, Inst. Hautes Études Sci. Publ. Math. 91 (2000), 55–131 (2001). MR 1828743
  • 4. E. Kowalski and P. Michel, The analytic rank of 𝐽₀(𝑞) and zeros of automorphic 𝐿-functions, Duke Math. J. 100 (1999), no. 3, 503–542. MR 1719730, 10.1215/S0012-7094-99-10017-2
  • 5. J. Wu, Average values of symmetric square $L$-functions at the edge of the critical strip, Proc. Amer. Math. Soc. 131 (2003), 1063-1070.

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Additional Information

Yuk-Kam Lau
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

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