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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cusp forms for congruence subgroups
of $Sp_n(\mathbb{Z})$ and theta functions


Author: Yaacov Kopeliovich
Journal: Trans. Amer. Math. Soc. 350 (1998), 3107-3118
MSC (1991): Primary 11F32
DOI: https://doi.org/10.1090/S0002-9947-98-01820-0
MathSciNet review: 1401524
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Abstract: In this paper we use theta functions with rational characteristic to construct cusp forms for congruence subgroups $\Gamma _g(p)$ of $Sp(g,\mathbb Z)$.The action of the quotient group $Sp(g,\mathbb Z_p)$ on these forms is conjugate to the linear action of $Sp(g,\mathbb Z_p)$ on $(\mathbb Z_p)^{2g}$. We show that these forms are higher-dimensional analogues of the Fricke functions.


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Additional Information

Yaacov Kopeliovich
Affiliation: Department of Mathematics, University of California, Irvine, California 92717
Address at time of publication: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: kopel@math.fsu.edu

DOI: https://doi.org/10.1090/S0002-9947-98-01820-0
Received by editor(s): October 17, 1995
Received by editor(s) in revised form: April 25, 1996
Article copyright: © Copyright 1998 American Mathematical Society