Kloosterman sums for Chevalley groups

On zeros of Kloosterman sums

A Note on Kloosterman Sums

has played an increasingly important role in the analytic theory of numbers. The dash ' beside the summation symbol indicates that the letter of summation runs only through a reduced residue system with respect to the modulus. The number h is defined as any solution of the congruence hh = l (mod k), and n denotes an arbitrary integer. It was shown by Salie almost fifteen years ago that Ak(n) ma...

Legendre Sums, Soto-andrade Sums and Kloosterman Sums

The three sums named in the title are all known to appear in connection with the complex representation theory of GL(2, q). The first two are incarnations of certain spherical vectors, whereas the third is a matrix coefficient for a parabolic basis. In this work, Legendre and Soto-Andrade sums are shown to occur in a second way, as parabolic ClebschGordan coefficients for the tensor product of ...

A New Bound for Kloosterman Sums

We give generating functions for Gauss sums for finite general linear and unitary groups. For the general linear case only our method of proof is new, but we deduce a bound on Kloosterman sums which is sometimes sharper than Deligne’s bound from algebraic geometry.

A Recursive Formula for Power Moments of 2-Dimensional Kloosterman Sums Assiciated with General Linear Groups

Abstract. In this paper, we construct a binary linear code connected with the Kloosterman sum for GL(2, q). Here q is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum, equivalently that generating the even power moments of Kloosterman sum in terms of the frequencies of weights in the code. This is done via Pless power moment identity ...