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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 20–53
DOI: https://doi.org/10.1134/S037196851603002X (Mi tm3725) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line

Olga G. Balkanovaa, Dmitry A. Frolenkovb

a Khabarovsk Division of the Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, ul. Dzerzhinskogo 54, Khabarovsk, 680000 Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (339 kB) Citations (5)
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DOI: https://doi.org/10.1134/S037196851603002X
Abstract: We prove an asymptotic formula for the second moment of primitive $L$-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift, and twist.
Funding agency Grant number
Russian Science Foundation 14-11-00335
14-50-00005
The work of O. G. Balkanova (Section 7 and in part Sections 1–5 and 8) is supported by the Russian Science Foundation under grant 14-11-00335 and performed in the Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences. The work of D. A. Frolenkov (Section 6 and in part Sections 1–5 and 8) is supported by the Russian Science Foundation under grant 14-50-00005 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.
Received: April 19, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 13–46
DOI: https://doi.org/10.1134/S008154381606002X
Bibliographic databases:
Document Type: Article
UDC: 511.321+511.331.1+511.381+511.384.6
Language: Russian
Citation: Olga G. Balkanova, Dmitry A. Frolenkov, “A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 20–53; Proc. Steklov Inst. Math., 294 (2016), 13–46
Citation in format AMSBIB
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\by Olga~G.~Balkanova, Dmitry~A.~Frolenkov
\paper A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line
\inbook Modern problems of mathematics, mechanics, and mathematical physics.~II
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 294
\pages 20--53
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S037196851603002X}
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  • https://doi.org/10.1134/S037196851603002X
  • https://www.mathnet.ru/eng/tm/v294/p20
    • This publication is cited in the following 5 articles:
    1. Balkanova O., “The First Moment of Maass Form Symmetric Squarel-Functions”, Ramanujan J., 55:2 (2021), 761–781  crossref  mathscinet  isi
    2. D. A. Frolenkov, “Nondiagonal terms in the second moment of automorphic $L$-functions”, Sb. Math., 211:8 (2020), 1171–1189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. D. Frolenkov, “The cubic moment of automorphic l-functions in the weight aspect”, J. Number Theory, 207 (2020), 247–281  crossref  mathscinet  zmath  isi
    4. O. Balkanova, D. Frolenkov, “Non-vanishing of automorphic $L$ -functions of prime power level”, Monatsh. Math., 185:1 (2018), 17–41  crossref  mathscinet  zmath  isi  scopus
    5. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line”, Izv. Math., 81:2 (2017), 239–268  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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