Eren Mehmet Kıral

Reduced word decompositions and Kloosterman sums

I will present progress on the joint work with Maki Nakasuji where we give a parametrization of double cosets of Bruhat cells inspired by the reduced word decomposition of Weyl group elements. As a result we give an explicit and nice expression of the long word GL(3) Kloosterman sum and also express the triple divisor sum function as a double Dirichlet series of exponential sums. Finally we point out a mistake regarding these sums in the previous literature.