| 摘要: |
| 本文研究了指数k-free数的特征函数qk（e）（n）（k ≥ 3）在square-full数集中的均值估计问题.利用黎曼Zeta函数的性质以及留数定理，获得了该均值的渐近公式，推广了qk（e）（n）在整数集中的均值估计相关结果. |
| 关键词: square-full数 留数定理 除数问题 Dirichlet卷积 均值 |
| DOI： |
| 分类号:O156.4 |
| 基金项目:南昌大学中国中部经济社会发展研究中心招标项目(15ZBLPS06)；江西高校哲学社会科学研究重大课题攻关项目(ZDGG02)；教育部哲学社会科学发展报告培育项目(13JBGP024). |
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| THE MEAN VALUE OF FUNCTION qk(e)(n) OVER SQUARE-FULL NUMBER |
|
YANG Li1,2,3, FU Chun3
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1.School of Management, Nanchang University, Nanchang 330031, China;2.School of Mathematics, Nanchang University, Nanchang 330031, China;3.Center for Central China Economic Development Research, Nanchang University, Nanchang 330031, China
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| Abstract: |
| In this paper, we study the mean value of the characteristic function qk(e)(n) of k-free over square-full number. By using the property of Riemann-Zeta function and residue theorem, we obtain the asymptotic formula of the mean value, which is the generalization of qk(e)(n)over integers. |
| Key words: square-full number residue theorem divisor problem Dirichlet convolution mean value |
