On the Mean Values of Certain Character Sums

Abstract

Let q≥5 be an odd number. In this paper, we study the fourth power mean of certain character sums ∑χmodq,χ-1=-1*∑1≤a≤q/4aχa4 and ∑χmodq,χ-1=1*∑1≤a≤q/4aχa4, where ∑‍* denotes the summation over primitive characters modulo q, and give some asymptotic formulae.