Mean value theorems for automorphic 𝐿-functions

Fomenko, O.

doi:10.1090/S1061-0022-08-01024-8

Mean value theorems for automorphic $L$-functions
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by O. M. Fomenko
Translated by: the author

St. Petersburg Math. J. 19 (2008), 853-866

DOI: https://doi.org/10.1090/S1061-0022-08-01024-8

Published electronically: June 27, 2008

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Abstract:

Let $f$ be a holomorphic Hecke eigencuspform of even weight $k\ge 12$ for $\operatorname {SL}(2, \mathbb {Z})$ and let $L(s, \operatorname {sym}^2f)$ be the symmetric square $L$-function of $f$. Let $C(x)$ be the summatory function of the coefficients of $L(s,\operatorname {sym}^2 f)$. The true order is found for \begin{equation*} \int ^{x}_{0}C(y)^2 dy. \end{equation*}

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