On a class of diagonal equations over finite fields

摘要

Using properties of Gauss and Jacobi sums, we derive explicit formulas for the number of solutions to a diagonal equation of the form x(1)(2m) + ... + x(n)(2m) = 0 over a finite field of characteristic p +/- 3 (mod 8). All of the evaluations are effected in terms of parameters occurring in quadratic partitions of some powers of p. (C) 2016 Elsevier Inc. All rights reserved.