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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
DOI: https://doi.org/10.1090/S0002-9939-03-07027-8
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?)

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  • 2. A. Ivic, ``The Riemann Zeta-Function,'' Wiley, New York, 1985. MR 87d:11062
  • 3. H. Iwaniec, W. Luo and P. Sarnak, Low lying zeros of families of $L$-functions, Inst. Hautes Études Sci. Publ. Math. 91 (2000), 55-131. MR 2002h:11081
  • 4. E. Kowalski and P. Michel, The analytic rank of $J\sb 0(q)$ and zeros of automorphic $L$-functions, Duke Math. J. 100 (1999), 503-542. MR 2001b:11060
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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: https://doi.org/10.1090/S0002-9939-03-07027-8
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

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