Given a root system Î¦ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums.â€¦ (More)

This paper describes a technique to construct Weyl group multiple Dirichlet series. Such series were first introduced in [BBC06], which also described a heuristic means to define, analyticallyâ€¦ (More)

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certainâ€¦ (More)

Let Î¦ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Î¦ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large,â€¦ (More)

We explicitly compute some double Dirichlet series constructed from n order Gauss sums over rational function fields. These turn out to be rational functions in qâˆ’s1 and qâˆ’s2 , where q is the size ofâ€¦ (More)

By a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with generating set given by choosing a generator for each cyclic factor. In this article we studyâ€¦ (More)

We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local field using lattice models from statistical mechanics. An explicit description of this Whittakerâ€¦ (More)

Friedberg, Hoffstein and Lieman have constructed two related multiple Dirichlet series from quadratic and higher-order L-functions and Gauss sums. We compute these multiple Dirichlet seriesâ€¦ (More)

Let n be an integer and let F be a nonarchimedean local field whose characteristic is not a prime dividing n. Let Î¼k be the group of k-th roots of unity in the algebraic closure of F ; we assume thatâ€¦ (More)

This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions. We begin by explaining how such series arise from Rankin-Selbergâ€¦ (More)