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

Action of Hecke operators on theta-functions with rational characteristics


Author: A. N. Andrianov
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 5.
Journal: St. Petersburg Math. J. 15 (2004), 715-732
MSC (2000): Primary 11F27, 11F46, 11F60, 11F66
Published electronically: August 2, 2004
MathSciNet review: 2068791
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Abstract | References | Similar Articles | Additional Information

Abstract: The explicit formulas for the transformation of theta-functions of integral positive definite quadratic forms under the action of regular Hecke operators, obtained in the author's earlier paper (1996), are converted to transformation formulas for the theta-functions with rational characteristics (the theta-series) viewed as Siegel modular forms. As applications, sequences of invariant subspaces and eigenfunctions for all regular Hecke operators on spaces of theta-series are constructed.


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Additional Information

A. N. Andrianov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023, Russia
Email: anandr@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-04-00828-3
PII: S 1061-0022(04)00828-3
Keywords: Hecke operators, Siegel modular forms, theta functions of quadratic forms, zeta functions of modular forms
Received by editor(s): April 23, 2003
Published electronically: August 2, 2004
Additional Notes: Supported in part by RFBR (grant no. 02-01-00087) and by SFB 478 “Geometrische Structuren in der Mathematik”, Westfälische Wilhelms-Universität Münster.
Article copyright: © Copyright 2004 American Mathematical Society