关于非正则三次域的戴德金ζ函数的均值的余项问题（英文）

On the Error Term for the Mean Value Associated With Dedekind Zeta-function of a Non-normal Cubic Field

设E_3/Q是一个非正则的三次扩域,a_k表示在域E_3上范数为k的整理想的个数R_x表示和式∑_(k≤x)a_k^2的渐近式的余项.本文证明了对任给的ε>0,∫_1~XR^2(x)dx■_εX^((65)/(27)+ε).

Let E3/Q be a non-normal cubic extension field, and let ak be the number of integral ideals in E3 with norm k. Denote R（x） by the remainder term in the asymptotic formula for the average behavior ∑k≤x ak^2. In this paper, it is shown that ∫1^X R^2（x）dx〈〈ε X^65/27＋ε.