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

Author(s): Yuk-Kam Lau
Journal: Proc. Amer. Math. Soc. 132 (2004), 317-323.
MSC (2000): Primary 11F67
Posted: June 17, 2003
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Abstract: Recently Wu proved that for all primes ,

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

where

runs over all normalized newforms of weight 2 and level

. Here we show that

can be replaced by

References:

1.: A. Akbary, Average values of symmetric square -functions at $\Re e\,s=2$ , C. R. Math. Rep. Acad. Sci. Canada 22 (2000), 97-104. MR 2001h:11067
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 -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 -functions, Duke Math. J. 100 (1999), 503-542. MR 2001b:11060
5.: J. Wu, Average values of symmetric square -functions at the edge of the critical strip, Proc. Amer. Math. Soc. 131 (2003), 1063-1070.


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