Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2010, Volume 88, Issue 3, Pages 456–475
DOI: https://doi.org/10.4213/mzm8817 (Mi mzm8817) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms

I. S. Rezvyakova

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (583 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm8817
Abstract: We consider an automorphic cusp form of integer weight $k\ge1$, which is the eigenfunction of all Hecke operators. It is proved that, for the $L$-series whose coefficients correspond to the Fourier coefficients of such an automorphic form, the positive fraction of nontrivial zeros lies on the critical line.
Keywords: automorphic cusp form, Riemann zeta function, Riemann hypothesis, Hecke operator, $L$-function, Jutila's circle method.
Received: 21.09.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 3, Pages 423–439
DOI: https://doi.org/10.1134/S0001434610090154
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: I. S. Rezvyakova, “On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms”, Mat. Zametki, 88:3 (2010), 456–475; Math. Notes, 88:3 (2010), 423–439
Citation in format AMSBIB
\Bibitem{Rez10}
\by I.~S.~Rezvyakova
\paper On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms
\jour Mat. Zametki
\yr 2010
\vol 88
\issue 3
\pages 456--475
\mathnet{http://mi.mathnet.ru/mzm8817}
\crossref{https://doi.org/10.4213/mzm8817}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2882185}
\transl
\jour Math. Notes
\yr 2010
\vol 88
\issue 3
\pages 423--439
\crossref{https://doi.org/10.1134/S0001434610090154}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000284073100015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78249277414}
Linking options:
  • https://www.mathnet.ru/eng/mzm8817
  • https://doi.org/10.4213/mzm8817
  • https://www.mathnet.ru/eng/mzm/v88/i3/p456
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024