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Twisted weyl group multiple Dirichlet series over the rational function field
In this thesis, we examine the relationship between Weyl group multiple Dirichlet series over the rational function field and their p-parts, which we define using the Chinta–Gunnells method . We show that these series may be written as the finite sum of their p-parts (after a certain variable change), with “multiplicities” that are character sums. Because the p-parts and global series are closely related, this result follows from a series of local results concerning the p-parts. In particular, we give an explicit recurrence relation on the coefficients of the p-parts, which allows us to extend the results of Chinta, Friedberg, and Gunnells . Additionally, we show that the p-parts of Chinta and Gunnells  agree with those constructed using the crystal graph technique of Brubaker, Bump, and Friedberg [4,5] (in the cases when both constructions apply).^
Friedlander, Holley Ann, "Twisted weyl group multiple Dirichlet series over the rational function field" (2013). Doctoral Dissertations Available from Proquest. AAI3603084.