Theta integrals and generalized error functions

Theta integrals and generalized error functions

###### Number Theory Seminar

#### Stephen Kudla (University of Toronto)

**Wednesday, October 4, 2017 -3:15pm to 4:15pm**

Recently Alexandrov, Banerjee, Manschot and Pioline constructed generalizations of Zwegers theta functions for lattices of signature (n-2,2). Their functions, which depend on two pairs of time like vectors, are obtained by `completing' a non-modular holomorphic generating series by means of a non-holomorphic theta type series involving generalized error functions. We show that their completed modular series arises as integrals of the 2-form valued theta functions, defined in old joint work of the author and John Millson, over a surface S determined by the pairs of time like vectors. This gives an alternative construction of such series and a conceptual basis for their modularity. If time permits, I will discuss the generalization to the case of arbitrary signature and a curious `convexity' problem for Grassmannians that arises in this context.