RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 20–53 (Mi tm3725)  

This article is cited in 2 scientific papers (total in 2 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

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.


DOI: https://doi.org/10.1134/S037196851603002X

Full text: PDF file (339 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 13–46

Bibliographic databases:

Document Type: Article
UDC: 511.321+511.331.1+511.381+511.384.6
Received: April 19, 2016

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, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 20–53; Proc. Steklov Inst. Math., 294 (2016), 13–46

Citation in format AMSBIB
\Bibitem{BalFro16}
\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 Tr. Mat. Inst. Steklova
\yr 2016
\vol 294
\pages 20--53
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3725}
\crossref{https://doi.org/10.1134/S037196851603002X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628491}
\elib{http://elibrary.ru/item.asp?id=26601049}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 294
\pages 13--46
\crossref{https://doi.org/10.1134/S008154381606002X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386554900002}
\elib{http://elibrary.ru/item.asp?id=27586854}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84992092088}


Linking options:
  • http://mi.mathnet.ru/eng/tm3725
  • https://doi.org/10.1134/S037196851603002X
  • http://mi.mathnet.ru/eng/tm/v294/p20

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  adsnasa  isi  elib
    2. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:223
    References:17
    First page:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019