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Action of Hecke operators on theta-functions with rational characteristics
Author(s):
A.
N.
Andrianov
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 5.
Journal:
St. Petersburg Math. J.
15
(2004),
715-732.
MSC (2000):
Primary 11F27, 11F46, 11F60, 11F66
Posted:
August 2, 2004
MathSciNet review:
2068791
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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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- 1.
- A. N. Andrianov, Multiplicative arithmetic of Siegel's modular forms, Uspekhi Mat. Nauk 34 (1979), no. 1, 67-135; English transl., Russian Math. Surveys 34 (1979), no. 1, 75-148. MR 0525651 (80f:10032)
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- 6.
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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:
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):
23/APR/2003
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
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