Reflective modular forms on lattices of prime level

Wang, Haowu

doi:10.1090/tran/8604

Reflective modular forms on lattices of prime level
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Trans. Amer. Math. Soc. 375 (2022), 3451-3468 Request permission

Abstract:

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.

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