Geodesic
Mean value theorems for automorphic $L$-functions
Algebra i analiz, Tome 19 (2007) no. 5, pp. 246-264.

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Let $f$ be a holomorphic Hecke eigencuspform of even weight $k\ge 12$ for $\mathrm{SL}(2, \mathbb{Z})$ and let $L(s,\mathrm{sym}^2f)$ be the symmetric square $L$-function of $f$. Let $C(x)$ be the summatory function of the coefficients of $L(s,\mathrm{sym}^2 f)$. The true order is found for $$ \int_0^x C(y)^2\,dy. $$
Keywords: Symmetric square $L$-function, summatory function, Euler product, Voronoi formula, mean value. 
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O. M. Fomenko. Mean value theorems for automorphic $L$-functions. Algebra i analiz, Tome 19 (2007) no. 5, pp. 246-264. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a9/

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