Geodesic
Nondiagonal terms in the second moment of automorphic $L$-functions
Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1171-1189

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We investigate the exact formula for the second moment of central $L$-values associated to primitive cusp forms of level one and weight $k\to\infty$, $k\in\mathbb N$, which was proved by Kuznetsov in 1994. Nondiagonal terms in this formula are expressed in terms of several convolution sums of divisor functions. We investigate the main terms of the convolution sums and show that they cancel out. Bibliography: 8 titles.
Keywords: moments of central values of $L$-functions, additive divisor problem, hypergeometric function. 
@article{SM_2020_211_8_a4,
     author = {D. A. Frolenkov},
     title = {Nondiagonal terms in the second moment of automorphic $L$-functions},
     journal = {Sbornik. Mathematics},
     pages = {1171--1189},
     publisher = {mathdoc},
     volume = {211},
     number = {8},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_8_a4/}
}
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D. A. Frolenkov. Nondiagonal terms in the second moment of automorphic $L$-functions. Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1171-1189. http://geodesic.mathdoc.fr/item/SM_2020_211_8_a4/