### Reduced word decompositions and Kloosterman sums

Linfoot Number Theory Seminar

4th December 2019, 11:00 am – 12:00 pm

Fry Building, 2.04

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.

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