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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 2, Pages 5–34 (Mi izv8426)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line

V. A. Bykovskiia, D. A. Frolenkovba

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We obtain new uniform asymptotic formulae for the second moments of $L$-series of cusp forms of even weight $2k\ge2$ with respect to the congruence subgroup $\Gamma_0(N)$.

Keywords: modular form, $L$-series of automorphic forms, convolution formula.

Funding Agency Grant Number
Russian Science Foundation 14-11-00335
The research was supported by the Russian Science Foundation (project no. 14-11-00335) in the Khabarovsk Division of the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences.


DOI: https://doi.org/10.4213/im8426

Full text: PDF file (754 kB)
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English version:
Izvestiya: Mathematics, 2017, 81:2, 239–268

Bibliographic databases:

UDC: 511.334+511.335
MSC: 11M06
Received: 06.07.2015
Revised: 25.03.2016

Citation: V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line”, Izv. RAN. Ser. Mat., 81:2 (2017), 5–34; Izv. Math., 81:2 (2017), 239–268

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Sb. Math., 208:5 (2017), 644–683  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. O. Balkanova, D. Frolenkov, “Bounds for a spectral exponential sum”, J. Lond. Math. Soc. (2), 99:2 (2019), 249–272  crossref  mathscinet  zmath  isi  scopus
    3. Y. Choie, W. Kohnen, Y. Zhang, “Simultaneous nonvanishing of products of l-functions associated to elliptic cusp forms”, J. Math. Anal. Appl., 486:2 (2020), 123930  crossref  mathscinet  zmath  isi
    4. V. A. Bykovskii, M. D. Monina, “Trace formula for integral points on the three-dimensional sphere”, Dokl. Math., 101:1 (2020), 9–11  crossref  isi
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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