广义四次Gauss和的四次均值

On the Fourth Power Mean of the Generalized Quartic Gauss Sums

本文利用解析方法以及经典Gauss和的性质,研究了模p为奇素数时广义四次Gauss和的四次均值的计算问题,并根据p≡3或1 mod 4,得到了该四次均值的一个精确计算公式和渐近公式.

The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of the fourth power mean of the generalized quartic Gauss sums mod p, an odd prime, and give an exact computational formula and asymptotic formula for it according to p ≡3 or 1 mod 4.