一类指数和的代数次数

Algebraic degrees of a class of exponential sums

摘要:

万大庆教授最近研究了高斯和S_q(f)的代数次数. 本文基于万大庆的结果研究了q=p^2及p模4余1情形的高斯和, 得到一类次数为1的高斯和S_q(x^d)的两种可能取值. 本文还推广了Myerson 在1981 年提出的方法, 进而得到了除d为奇数的某些特定情形外所有高斯和代数次数的准确值.

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.