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

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- by Yaacov Kopeliovich PDF
- Trans. Amer. Math. Soc.
**350**(1998), 3107-3118 Request permission

## 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.## References

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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
- Received by editor(s): October 17, 1995
- Received by editor(s) in revised form: April 25, 1996
- © Copyright 1998 American Mathematical Society
- 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