Reflective modular forms on lattices of prime level

Abstract

One of the main open problems in the theory of automorphic products is to classify reflective modular forms. In [Sch06] Scheithauer classified strongly reflective modular forms of singular weight on lattices of prime level. In this paper we classify symmetric reflective modular forms on lattices of prime level. This yields a full classification of lattices of prime level which have reflective modular forms. We also present some applications.

Final version, to appear in Trans. Amer. Math. Soc

References in corpus (2)

• The classification of 2-reflective modular forms
• Antisymmetric paramodular forms of weight 3

Cited by in corpus (1)

• Maximal Discrete Subgroups of $S{O}^{+}(2,n+2)$