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

Journal article, 2015

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