Geodesic
Identities involving the coefficients of automorphic $L$-functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 247-256

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Let $f(z)$ be a holomorphic Hecke eigenform of weight $k$ with respect to $SL(2,\mathbb Z)$ and let $$ L(s,\operatorname{sym}^2f)=\sum\limits^{\infty}_{n=1}c_n n^{-s},\quad \operatorname{Re}s>1, $$ denote the symmetric square $L$-function of $f$. A Voronoi type formula for $$ C(x)=\sum\limits_{n\leqslant x}c_n. $$ and the relation $$ C(x)=\Omega_{\pm}(x^{1/3}). $$ are proved. Heuristic approaches to estimation of exponential sums arising in this connection are considered. 
@article{ZNSL_2004_314_a14,
     author = {O. M. Fomenko},
     title = {Identities involving the coefficients of automorphic $L$-functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {247--256},
     publisher = {mathdoc},
     volume = {314},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a14/}
}
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O. M. Fomenko. Identities involving the coefficients of automorphic $L$-functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 247-256. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a14/