Joint IAS/Princeton University Number Theory Seminar

Weyl group multiple Dirichlet series are multiple Dirichlet series in 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 Eisenstein 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.