Mathematical Research Letters
Volume 22 (2015)
The structure of Siegel modular forms modulo $p$ and $U(p)$ congruences
Pages: 899 – 928
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