Algebraic degrees of a class of exponential sums

Abstract:

Recently Wan studied the algebraic degrees of the exponential sums S_q(f) over a finite field F_q. In this article, basing on Wan's results, we discuss the Gauss sums for the case q=p^2 and obtain that S_q(x^d) has only two possible values, if it is of degree 1. Additionlly we generalize a method proposed by Myerson in 1981 and get all explicit values of the algebraic degrees of Gauss sums in some special cases.