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

Lau, Yuk-Kam

doi:10.1090/S0002-9939-03-07027-8

On the error term in an asymptotic formula for the symmetric square $L$-function
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Proc. Amer. Math. Soc. 132 (2004), 317-323 Request permission

Abstract:

Recently Wu proved that for all primes $q$, \[ \sum _{f} L(1, \mbox {sym}^2f) =\frac {\pi ^4}{432}q +O(q^{27/28}\log ^B q) \] 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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