  We give an axiomatic characterization of multiple Dirichlet series over the
function field $\mathbb F_q(T)$, generalizing a set of axioms given by Diaconu
and Pasol. The key axiom, relating the coefficients at prime powers to sums of
the coefficients, formalizes an observation of Chinta. The existence of
multiple Dirichlet series satisfying these axioms is proved by exhibiting the
coefficients as trace functions of explicit perverse sheaves and using
properties of perverse sheaves. The multiple Dirichlet series defined this way
include, as special cases, many that have appeared previously in the
literature.
