Everytopic Seminar

 November 14th, 2008, 1:40 pm – 3:00pm, Goldsmith 226


Title: Weyl Group Multiple Dirichlet Series

Speaker: Paul Gunnells, University of Massachusetts at Amherst



Multiple Dirichlet series are generalizations of L-functions

involving several complex variables.  While the functional equation

of a usual L-series is an involution s -> 1-s, a multiple

Dirichlet series satisfies a group of functional equations that

intermixes all the variables.  


In this talk we give examples of multiple Dirichlet series and their

applications.  We will show how consideration of these series arises

naturally in number theoretic applications.  Then we describe a

construction of Weyl group multiple Dirichlet series.  These are

series attached to root systems plus some extra data where the

resulting group of functional equations is the associated Weyl group.

In general these series are expected to be Whitaker-Fourier

coefficients of metaplectic Eisenstein series, although that is not

how the series are defined.  An essential part of the construction is

a deformation of the Weyl character formula for the associated

semisimple complex Lie algebra.

This is joint work with Gautam Chinta.