二次代数扩域上理想计数函数在短区间上的均值估计

Mean Value Estimation of Ideal Counting Function in Short Interval over Quadratic Algebraic Extension Field

设K是有理数域的二次代数扩张,aK(n)是K上的理想计数函数,本文利用Selberg-Delange方法给出aK(n)l在短区间n∈[x,x+y]上的均值估计如下:对于一致成立,其中c,c1,c2均为与l有关的常数。Let K be a quadratic algebraic extension of , aK(n) is an ideal counting function on K. In this paper, we use the Selberg-Delange method to give the mean estimation of aK(n)l in a short interval as follows: It is consistent for where c,c1,c2 are constants related to l.