REFLECTIVE MODULAR FORMS ON LATTICES OF PRIME LEVEL

One of the main open problems in the theory of automorphic products is to classify reflective modular forms. Scheithauer [Invent. Math. 164 (2006), pp. 641-678] 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.

Automated summary

This paper focuses on the classification of reflective modular forms, which is one of the main open problems in the theory of automorphic products. The author previously classified strongly reflective modular forms with singular weight on lattices of prime level. In this paper, the author extends the classification to symmetric reflective modular forms on lattices of prime level. This provides a complete classification of lattices of prime level that have reflective modular forms, and also presents some applications.