English

On the converse theorem for Borcherds products

Number Theory 2012-10-18 v1 Algebraic Geometry

Abstract

We prove a new converse theorem for Borcherds' multiplicative theta lift which improves the previously known results. To this end we develop a newform theory for vector valued modular forms for the Weil representation, which might be of independent interest. We also derive lower bounds for the ranks of the Picard groups and the spaces of holomorphic top degree differential forms of modular varieties associated to orthogonal groups.

Keywords

Cite

@article{arxiv.1210.4821,
  title  = {On the converse theorem for Borcherds products},
  author = {Jan Hendrik Bruinier},
  journal= {arXiv preprint arXiv:1210.4821},
  year   = {2012}
}

Comments

29 pages

R2 v1 2026-06-21T22:23:28.973Z