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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Zeta-functions of harmonic theta-series and prime numbers
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by A. Andrianov
Translated by: the author
St. Petersburg Math. J. 23 (2012), 239-255
DOI: https://doi.org/10.1090/S1061-0022-2012-01195-7
Published electronically: January 23, 2012
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Abstract:

The problem of finding Euler product expansions is treated for zeta-functions of modular forms in one variable that are presented by harmonic theta-series. On the basis of the author’s formulas obtained earlier for the action of the Hecke operators on harmonic theta-functions, Euler product expansions are obtained for eigenfunctions of Hecke operators. For the theta-series of quadratic forms proportional to the sum of two squares, the eigenfunctions of Hecke operators are constructed and the associated Euler expansions are calculated.
References
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Bibliographic Information
  • A. Andrianov
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
  • Address at time of publication: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
  • Email: anatoli.andrianov@gmail.com, andriano@mpim-bonn.mpg.de
  • Received by editor(s): October 12, 2010
  • Published electronically: January 23, 2012
  • Additional Notes: The author was supported in part by RFBR (grant 08-01-00233).
  • © Copyright 2012 American Mathematical Society
  • Journal: St. Petersburg Math. J. 23 (2012), 239-255
  • MSC (2010): Primary 11F27; Secondary 11F46, 11F60, 14G10, 20C08
  • DOI: https://doi.org/10.1090/S1061-0022-2012-01195-7
  • MathSciNet review: 2841672