Problem 4 : root systems , highest-weight polytopes , and exponential sums

In this paper, we consider the Dirichlet series that comes from the process of obtaining the Whittaker coefficients for the maximal parabolic Eisenstein series, outlined in from Brubaker and Friedberg’s paper [BF15] in the case of the Dynkin diagram of A5. Specifically, we take the maximal parabolic corresponding to the removal of the second simple root from A5. We compute the support of the exponential sum corresponding to this removal of the second simple root from A5, in order to see how the Dirichlet series to another Dirichlet series associated to A5 outlined in Chinta’s paper [Chi05].