Structure of Hermitian modular forms modulo \(p\) and some applications (Q2045743)

The paper under review generalizes some known congruences for Siegel modular forms to Hermitian modular forms. Specifically, the authors determine the ring structure of Hermitian modular forms of degree \(2\) modulo a prime \(p\) (see Thm~1.1 and Cor~1.2). Moreover, the authors consider the theta operator \(\Theta\) for Hermitian modular forms, and prove that if \(F\) is a Hermitian cusp form of weight \(k\) that does not vanish modulo a prime \(p\) with \(p>k\), then \(\Theta(F)\) does not vanish modulo \(p\) (see Thm~1.3).