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Mat. Sb., 2020, Volume 211, Number 8, Pages 114–131 (Mi msb9313)  

Nondiagonal terms in the second moment of automorphic $L$-functions

D. A. Frolenkovab

a Pacific National University, Khabarovsk
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 18-41-05001
This research was carried out at Pacific National University and supported by the Russian Science Foundation under grant no. 18-41-05001.


DOI: https://doi.org/10.4213/sm9313

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English version:
Sbornik: Mathematics, 2020, 211:8, 1171–1189

UDC: 511.334+517.588
MSC: Primary 11F12; Secondary 11F66
Received: 08.08.2019 and 19.03.2020

Citation: D. A. Frolenkov, “Nondiagonal terms in the second moment of automorphic $L$-functions”, Mat. Sb., 211:8 (2020), 114–131; Sb. Math., 211:8 (2020), 1171–1189

Citation in format AMSBIB
\Bibitem{Fro20}
\by D.~A.~Frolenkov
\paper Nondiagonal terms in the second moment of automorphic $L$-functions
\jour Mat. Sb.
\yr 2020
\vol 211
\issue 8
\pages 114--131
\mathnet{http://mi.mathnet.ru/msb9313}
\crossref{https://doi.org/10.4213/sm9313}
\transl
\jour Sb. Math.
\yr 2020
\vol 211
\issue 8
\pages 1171--1189
\crossref{https://doi.org/10.1070/SM9313}


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