Title: Multiple Dirichlet series attached to Weyl groups
Weyl group multiple Dirichlet series are multiple Dirichlet
several variables whose coefficients involve Gauss sums and
also reflect the combinatorics of a given root system.
The earliest examples came from Mellin transforms of metaplectic
series and have been intensively studied over the last 20 years. These
functions and their residues unify and generalize a number of
examples which have been previously treated individually,
often with applications to analytic number theory.
In this lecture I give an account of some of the major research to date
and the opportunities for the future.