| We give explicit computations of a pair of double Dirichlet series first studied by the Friedberg, Hoffstein, and Lieman. These computations are performed in the rational function field because, in this context, the series are power series which turn out to be rational functions.;Recently the Weyl group multiple Dirichlet series have been an area of intense research. We provide an explicit computation for these series associated to the root system of type Ar, again in the rational function field case. This shows the equivalence of two different descriptions of the local parts of these series and establishes uniqueness. It is conjectured that a multiresidue of the Weyl group multiple Dirichlet series correspond with the double Dirichlet series first noted of Friedberg, Hoffstein, and Lieman. This conjecture is proven in the rational function field case using the computed rational functions. |
