Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu g**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: An Arithmetic Ansatz for the Singularities of Hypergeometric Multisums

Speaker: **Stavros Garoufalidis**, Georgia Tech

Date: Thursday, March 29, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

A special term is a product of binomials of linear forms in many variables. It is known that the generating series of a special term is convergent near the origin and satisfies a linear ODE with polynomial coefficients. There are three proofs of this property, although they are all computationally costly, for multisums. In the talk we will give a simple ansatz for the singularities of the generating series. We will also give a proof of our ansatz in case the special term is positive, and an illustration our ansatz with the Apery series, responsible for the irrationality of zeta(3). Our ansatz is reminiscent of the Bethe ansatz, and has a motivic interpretation using additive K-theory. If you don't know what these are, you won't loose much!