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Sbornik: Mathematics, 2020, Volume 211, Issue 8, Pages 1171–1189
DOI: https://doi.org/10.1070/SM9313 (Mi sm9313) 		 
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
English version PDF (496 kB) Russian version article
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DOI: https://doi.org/10.1070/SM9313
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.
Received: 08.08.2019 and 19.03.2020
Bibliographic databases:
Document Type: Article
UDC: 511.334+517.588
MSC: Primary 11F12; Secondary 11F66
Language: English
Original paper language: Russian
Citation: D. A. Frolenkov, “Nondiagonal terms in the second moment of automorphic $L$-functions”, Sb. Math., 211:8 (2020), 1171–1189
Citation in format AMSBIB
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\yr 2020
\vol 211
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\pages 1171--1189
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