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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Zeta-functions of harmonic theta-series and prime numbers


Author: A. Andrianov
Translated by: the author
Original publication: Algebra i Analiz, tom 23 (2011), nomer 2.
Journal: St. Petersburg Math. J. 23 (2012), 239-255
MSC (2010): Primary 11F27; Secondary 11F46, 11F60, 14G10, 20C08
Published electronically: January 23, 2012
MathSciNet review: 2841672
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01195-7
PII: S 1061-0022(2012)01195-7
Keywords: Euler products, harmonic theta-functions and theta-series, Hecke operators, prime numbers, zeta-functions of theta-functions and theta-series
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).
Article copyright: © Copyright 2012 American Mathematical Society