On the converse theorem for Borcherds products

By Jan H. Bruinier. 2012

75 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f68e8eec1115746e2abe70c47ecd36679d58e31