Borcherds products of half-integral weight

TL;DR

This paper establishes a precise criterion for the existence of Borcherds products of half-integral weight linked to even lattices, demonstrating their existence across lattices of any rank.

Contribution

It provides a necessary and sufficient condition for constructing half-integral weight Borcherds products for lattices splitting two hyperbolic planes.

Findings

Existence criterion for half-integral weight Borcherds products

Proof of existence for arbitrary rank lattices

Application to even lattices splitting hyperbolic planes

Abstract

We give a necessary and sufficient criterion for the existence of Borcherds products of half-integral weight associated to even lattices that split two hyperbolic planes. In particular we prove that half-integral weight Borcherds products exist for lattices of arbitrary rank.