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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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Action of Hecke operators on theta-functions with rational characteristics
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by A. N. Andrianov
Translated by: the author
St. Petersburg Math. J. 15 (2004), 715-732
DOI: https://doi.org/10.1090/S1061-0022-04-00828-3
Published electronically: August 2, 2004
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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.
References
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Bibliographic 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
  • 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.
  • © Copyright 2004 American Mathematical Society
  • Journal: St. Petersburg Math. J. 15 (2004), 715-732
  • MSC (2000): Primary 11F27, 11F46, 11F60, 11F66
  • DOI: https://doi.org/10.1090/S1061-0022-04-00828-3
  • MathSciNet review: 2068791