一类特征和的上界估计

Estimation of Upper Bound for a Kind of Character Sums

研究某一类有理函数的特征和∑χff21(x)的上界估计,通过引入Burgess的一个有关"集合的势"的命题,并经过一系列关于集合的初等变换,得到在某些特定集合上一类有理函数特征和的上界估计.该估计在一部分区间上改进了刘春雷所获得的一般性结论,而且相比于Burgess对相同类型结论的证明步骤,还作了极大的简化.本结论还可用于进一步研究r=4时短区间上特征和的上界估计.

The upper bound of the character sum of a certain kind of rational function∑x（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.