Kloosterman sums and finite field extensions

On Kloosterman sums over finite fields of characteristic 3

We study the divisibility by 3 of Kloosterman sums K(a) over finite fields of characteristic 3. We give a simple recurrent algorithm for finding the largest k, such that 3 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

Sum-product Estimates in Finite Fields via Kloosterman Sums

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

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 ...

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...