序列[n^c]上多维除数函数的和

The Sum of Multidimensional Divisor Function on a Sequence of Type[n^c]

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摘要设[θ]表示θ的整数部分,k≥2,dk(n)为除数函数.证明了当实数c满足1<c<3849/3334时,∑d_k([n^c])具有渐近公式,从而改进了吕广世和翟文广的结果(1<c<495/433),而且当k=2时,n≤x实数c的范围可以改进到1<c<391/335. Let[θ]be the integral part ofθand k≥2,d_k（n） denote the divisor function. In this paper it is proved that d_k（[n^c]） has an asymptotic formula when 1c3849/3334, which improves L（u｜¨） Guangshi and Zhai Wenguang＇s result 1c495/433.Moreover,if k = 2, then the range of c can be enlarged to 1c391/335.

作者李英杰

机构地区上海海洋大学信息学院

出处《数学年刊（A辑）》 CSCD 北大核心 2011年第3期355-364,共10页 Chinese Annals of Mathematics

基金上海高校选拔培养优秀青年教师科研专项基金(No.ssc08017) 上海海洋大学博士科研启动基金资助的项目

关键词除数函数渐近公式指数和指数对 Divisor function Asymptotic formula Exponential sum Exponent pair

分类号 O156.4 [理学—基础数学]

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参考文献18

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二级参考文献6

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1吕广世,翟文广.关于特殊序列上的多维除数函数的和[J].数学进展,2003,32(6):660-664. 被引量：1
2牟全武.一个素变量丢番图不等式（英文）[J].数学进展,2015,44(4):621-637.

数学年刊（A辑）

2011年第3期

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序列[n^c]上多维除数函数的和

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