Reflective automorphic forms on lattices of squarefree level

TL;DR

This paper classifies all nonconstant reflective automorphic forms on certain lattices, showing finiteness and providing a complete list under specific conditions related to zeros and weight.

Contribution

It establishes the finiteness of such forms and fully classifies those with simple zeros and singular weight on lattices of squarefree level.

Findings

Finiteness of nonconstant reflective automorphic forms on specified lattices.

Complete classification for forms with simple zeros and singular weight.

Identification of all such forms under the given conditions.

Abstract

We show that there are only finitely many nonconstant reflective automorphic forms $\Psi$ on even lattices of squarefree level splitting two hyperbolic planes and give a complete classification in the case where the zeros of $\Psi$ are simple and $\Psi$ has singular weight.