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Colloquium: More products for Borcherds forms September 29, 2014 (04:00 PM PDT - 05:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Stephen Kudla (University of Toronto)
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In a pair of Invenitones papers in 1995 and 1998, Borcherds gave a construction of meromorphic modular forms on the hermitian symmetric domain associated to a rational quadratic space V, ( , )  of signature (n,2).  These modular forms have remarkable properties including

(1) an explicit divisor given in terms of special divisors and

(2) product formulas, each valid in a neighborhood of a point boundary component.

In this lecture, after reviewing Borcherds' construction, and under the assumption that V, ( , ) admits 2-dimensional rational isotropic subspaces,  I will describe some new product formulas for these modular forms, each valid in the neighborhood of a 1-dimensional boundary component. The products involve Jacobi theta functions and eta functions.

They should prove useful in understanding the integral theory of Borcherds forms.

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