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

Twisting of Siegel modular forms with characters, and $ L$-functions


Author: A. Andrianov
Translated by: the author
Original publication: Algebra i Analiz, tom 20 (2008), nomer 6.
Journal: St. Petersburg Math. J. 20 (2009), 851-871
MSC (2000): Primary 11F46, 11F60, 11F66
Published electronically: October 1, 2009
MathSciNet review: 2530893
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-09-01076-0
PII: S 1061-0022(09)01076-0
Keywords: Hecke operators, Siegel modular forms, zeta-functions of modular forms
Received by editor(s): June 2, 2008
Published electronically: October 1, 2009
Additional Notes: Supported in part by RFBR (grant no. 08-01-00233)
Article copyright: © Copyright 2009 American Mathematical Society