Borcherds products with prescribed divisor
Number Theory
2017-09-27 v2
Abstract
Given an infinite set of special divisors satisfying a mild regularity condition, we prove the existence of a Borcherds product of non-zero weight whose divisor is supported on these special divisors. We also show that every meromorphic Borcherds product is the quotient of two holomorphic ones. The proofs of both results rely on the properties of vector valued Eisenstein series for the Weil representation.
Keywords
Cite
@article{arxiv.1607.08713,
title = {Borcherds products with prescribed divisor},
author = {Jan Hendrik Bruinier},
journal= {arXiv preprint arXiv:1607.08713},
year = {2017}
}
Comments
Proof of Theorem 2.1 added in v2