Mathematical Research Letters

Volume 22 (2015)

Number 3

The structure of Siegel modular forms modulo $p$ and $U(p)$ congruences

Pages: 899 – 928



Martin Raum (Department of Mathematics, ETH Zürich, Switzerland)

Olav K. Richter (Department of Mathematics, University of North Texas, Denton, Tx., U.S.A.)


We determine the ring structure of Siegel modular forms of degree $g$ modulo a prime $p$, extending Nagaoka’s result in the case of degree $g = 2$. We characterize $U(p)$ congruences of Jacobi forms and Siegel modular forms, and surprisingly find different behaviors of Siegel modular forms of even and odd degrees.


Siegel modular forms modulo $p$, theta cycles and $U(p)$ congruences, Jacobi forms modulo $p$

2010 Mathematics Subject Classification

Primary 11F33, 11F46. Secondary 11F50.

Accepted 14 August 2014

Published 20 May 2015