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
DOI:
https://doi.org/10.1090/S1061-0022-2012-01195-7
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
Email:
anatoli.andrianov@gmail.com, andriano@mpim-bonn.mpg.de
DOI:
https://doi.org/10.1090/S1061-0022-2012-01195-7
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
