| k-free数与其逆的差 |
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| 引用本文： | 代志杰.k-free数与其逆的差[J].纺织高校基础科学学报,2014(1):54-57. |
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| 作者姓名： | 代志杰 |
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| 作者单位： | 西北大学数学系,陕西西安710127 |
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| 摘 要： | 运用Kloosterman和、特征和以及三角和的一些基本性质和估计得到了k-free数与其逆的差的一个渐近公式.并且证明了:当k≥2,m≥2,n2,n∈N,k∈N,m∈N,ε0时,M(n,m;k)=2φ(n)nm/ζ2(k)(m+1)(m+2)+O(2mnm+1/2+2/(k+1)+2εd(n)σ-1/2(n)σ(n)).特别是当k=2时,有无平方因子数与其逆的差:M(n,m;2)=72φ(n)nm/π4(m+1)(m+2)+O(2mnm+1/2+2/(k+1)+2εd(n)σ-1/2(n)σ(n).此处的d(n)表示因数函数,(n)表示欧拉函数.
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| 关 键 词： | 指数和 k-free数 三角和 |
On the difference of k-free integer and its inverse |
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| DAI Zhi-jie.On the difference of k-free integer and its inverse[J].Basic Sciences Journal of Textile Universities,2014(1):54-57. |
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| Authors: | DAI Zhi-jie |
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| Affiliation: | DAI Zhi-jie ( Department of Mathmatics, Northwest University, Xi＇ an 710127, China) |
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| Abstract: | By using character sums ,kloosterman sums and some basic properties of the triangle sums ,an asymptotic formula was achieved .And the difference of square free number and its inverse were proved . |
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| Keywords: | exponent sums k-free interger triangle sums |
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