Kloosterman sums and Bessel functions (Robert Cass, CMC)

Kloosterman sums are explicit exponential sums which occur in several contexts in number theory and arithmetic geometry. Bessel functions encode a great deal of representation-theoretic information about finite groups of Lie type, but they are difficult to compute in general. In this talk, we will carefully define these objects and describe a direct relationship between them. One of our main goals is to provide many explicit examples, including ones for the exceptional groups E6 and E7.