Mean value theorems for automorphic $L$-functions

Type: Article

Publication Date: 2008-06-27

Citations: 16

DOI: https://doi.org/10.1090/s1061-0022-08-01024-8

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*}

Locations

  • St Petersburg Mathematical Journal - View - PDF

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