4/12/2006

Stephen Kudla
Institute for Advanced Study

Singular moduli

In this lecture, I will describe some results from the thesis of Jarad Schofer, (Maryland, 2005), which provide a generalization of the Gross-Zagier factorization of singular moduli for arbitrary Borcherds forms. After a review of the construction of Borcherds forms in an adelic setting and their general properties, I will explain how the factorization formula can be obtained by applying a seesaw identity, the Siegel-Weil formula, Maass operators and a Stokes theorem calculation.