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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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Twisting of Siegel modular forms with characters, and $L$-functions
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by A. Andrianov
Translated by: the author
St. Petersburg Math. J. 20 (2009), 851-871
DOI: https://doi.org/10.1090/S1061-0022-09-01076-0
Published electronically: October 1, 2009
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Abstract:

Linear twistings of Siegel modular forms with Dirichlet characters are considered. It is shown that the twisting operators transform modular forms to modular forms. Commutation of twisting operators and Hecke operators is examined. It is proved that under certain conditions the spinor zeta-function of a twisted modular form can be interpreted as the $L$-function of the initial modular form with twisting character. As an illustration of the twist techniques, analytic properties of $L$-functions of cusp forms of genus $n=1$ are considered.
References
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Bibliographic Information
  • A. Andrianov
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
  • Email: anandr@pdmi.ras.ru, anatoli.andrianov@gmail.com
  • Received by editor(s): June 2, 2008
  • Published electronically: October 1, 2009
  • Additional Notes: Supported in part by RFBR (grant no.ย 08-01-00233)
  • © Copyright 2009 American Mathematical Society
  • Journal: St. Petersburg Math. J. 20 (2009), 851-871
  • MSC (2000): Primary 11F46, 11F60, 11F66
  • DOI: https://doi.org/10.1090/S1061-0022-09-01076-0
  • MathSciNet review: 2530893