Study on a new divisor problem arisen from the derivatives of the Riemann zeta function

这一研究是经典Dirichlet因子问题的新发展。设d(N)是n的除数(称为除数函数)。在d(N)的平均值中，研究误差项称为除数问题。从Riemann Zeta函数导数的研究出发，定义了一个新的除数函数D(K)(N)。通过这一研究，我们得到了D(K)(N)的平均误差项的公式。它由贝塞尔函数的某个有限和来表示。

This research is a new development on the classical Dirichlet divisor problem. Let d(n) be the number of divisor of n (it is called the divisor function). In the average of d(n), to study the error term is called the divisor problem. From an aspect of the study of the derivatives of Riemann zeta function, we define a new divisor function D(k)(n). By this research we obtained a formula on the error term in the average of D(k)(n). It is expressed by a certain finite sum of Bessel functions.