Abstract:

The upper bound of the character sum of a certain kind of rational function ∑χ ((f₁/f₂)(x))  has been studied. By introducing Burgess’s proposition about the cardinal number of sets and making a series of elementary set transformation, the result of the estimation of some particular sets is obtained. It partly improves Liu’s result, and simplifies the previous proof given by Burgess in proving the same kind of character sums. Moreover, the result presented in this paper is favorable in further estimating character sums in short intervals when r=4 following Burgess.

Key words: Dirichlet character; character sums; rational function