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On the converse theorem for Borcherds products

2013; Elsevier BV; Volume: 397; Linguagem: Inglês

10.1016/j.jalgebra.2013.08.034

1090-266X

Jan Hendrik Bruinier,

Advanced Mathematical Identities

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.