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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 | References | Similar Articles | Additional Information

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

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