On the $p$-parts of Weyl group multiple Dirichlet series
Volume 179 / 2017
Acta Arithmetica 179 (2017), 301-317
MSC: Primary 11F68, 11M41; Secondary 20F55.
DOI: 10.4064/aa8309-5-2017
Published online: 11 July 2017
Abstract
We study the structure of $p$-parts of Weyl group multiple Dirichlet series. In particular, we extend results of Chinta, Friedberg, and Gunnells (2008) and show, in the stable case, that the $p$-parts of Chinta and Gunnells (2010) agree with those constructed using the crystal graph technique of Brubaker, Bump, and Friedberg (2006, 2008). In this vein, we give an explicit recurrence relation on the coefficients of the $p$-parts, which allows us to describe the support of the $p$-parts and address the extent to which they are uniquely determined.
