English

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

R2 v1 2026-06-22T15:07:29.217Z