Reflective modular forms on lattices of prime level

Wang, Haowu

doi:10.1090/tran/8604

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Reflective modular forms on lattices of prime level

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Wang, Haowu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/tran/8604
(Publisher version)

https://doi.org/10.48550/arXiv.1912.11220
(Preprint)

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Citation

Wang, H. (2022). Reflective modular forms on lattices of prime level. Transactions of the American Mathematical Society, 375(5), 3451-3468. doi:10.1090/tran/8604.

Cite as: https://hdl.handle.net/21.11116/0000-000A-2226-5

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.