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.
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