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Weyl group multiple Dirichlet series are Dirichlet series in $r$ complexvariables, with analytic continuation to $\mathbb{C}^r$ and a group offunctional equations isomorphic to the Weyl group of a reduced root system ofrank $r$. Such series may be defined for any global field $K$, but in the casewhen $K$ is an algebraic function field they are expected to be, up to avariable change, rational functions in several variables. We verify therationality of these functions in the case when $K=\mathbb{F}_q(T)$, anddescribe the denominators and support of the numerators.

Twisted Weyl group multiple Dirichlet series over the rational function field