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 [10]. 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 [9]. Additionally, we show that the p-parts of Chinta and Gunnells [10] agree with those constructed using the crystal graph technique of Brubaker, Bump, and Friedberg [4,5] (in the cases when both constructions apply).
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-7099 |
| Date | 01 January 2013 |
| Creators | Friedlander, Holley Ann |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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