Weyl group multiple Dirichlet series of type A_2
Number Theory
2007-05-23 v1
Abstract
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Phi. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n-th order Gauss sums attached to the root system of type A_2. The basic technique is to construct a rational function in r variables invariant under a certain action of W, and use this to build a ``local factor'' of the global series.
Cite
@article{arxiv.math/0703040,
title = {Weyl group multiple Dirichlet series of type A_2},
author = {Gautam Chinta and Paul E. Gunnells},
journal= {arXiv preprint arXiv:math/0703040},
year = {2007}
}