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[1]黄勇庆,刘 双.无平方因子整数上的反正弦律[J].绵阳师范学院学报,2018,(02):16-21,55.[doi:10.16276/j.cnki.cn51-1670/g.2018.02.004]
 HUANG Yongqing,LIU Shuang.On the Arcsine Law over Square-free Numbers[J].Journal of Mianyang Normal University,2018,(02):16-21,55.[doi:10.16276/j.cnki.cn51-1670/g.2018.02.004]
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《绵阳师范学院学报》[ISSN:1672-612X/CN:51-1670/G]

卷:
期数:
2018年02期
页码:
16-21,55
栏目:
数学与统计
出版日期:
2018-02-25

文章信息/Info

Title:
On the Arcsine Law over Square-free Numbers
文章编号:
1672-612X(2018)02-0016-06
作者:
黄勇庆1 刘 双2
1.重庆市第一中学校, 重庆市沙坪坝区 400030;
2.重庆工业职业技术学院基础教学部,重庆渝北 401120
Author(s):
HUANG Yongqing1 LIU Shuang2
1.Chongqing No.1Middle School, Chongqing 40030;
2.Department of Basic Courses, Chongqing Industry Polytechnical College, Yubei, Chongqing 401120
关键词:
Selberg-Delange方法 反正弦律 无平方因子整数
Keywords:
Selberg-Delange method arcsine law square-free numbers
分类号:
O156.4
DOI:
10.16276/j.cnki.cn51-1670/g.2018.02.004
文献标志码:
A
摘要:
本文研究因子函数的Cesaro均值,并证明了反正弦律在无平方因子整数上成立,该结果可看作是Deshouillers, Dress和Tenenbaum结果的推广.
Abstract:
In this paper, we study the Cesaro means related to the divisor function. We show that the arcsine law holds over square-free numbers, which generalizes theresult investigated by Deshouillers, Dress and Tenenbaum.

参考文献/References:

[1] Bin. Feng, On the arcsine law on divisors in arithmetic progressions. Indagationes Mathematicae, 2016.27: 749-763.
[2] Cui Z.,Wu J..The Selberg-Delange method in short intervals with an application. Acta Arith, 2014,163(3):247-260.
[3] Deshouillers J.-M., Dress F., Tenenbaum G..Lois de repartition des diviseurs,1, Acta Arith, 1979,23: 273-283.
[4] Delange H., Sur les formules dues a Atle Selberg, Bull. Sci. Math. serie, 1959,83:101-111.
[5] Delange H., Sur les formules de Atle Selberg. Acta Arith, 1971(19 ):105-146.
[6] Hanrot G., Tenenbaum G. Wu J.. Moyennes de certaines fonctions arithmetiques sur les entiers friables(2)Proc. London Math. Soc, 2008,96(3):107-135.
[7] Huxley M. N.. The difference between consecutive primes. Inven. Math, 1972(15 ):164-170.
[8] Lau Y.-K.. Summatory formula of the convolution of two arithmetical functions, Monatsh. Math, 2002,136(1):35-45.
[9] Lau Y.-K., Wu J.. Sums of some multiplicative functions over a special set of integers. Acta Arith, 2002,101(4):365-394.
[10] Selberg A.Note on the paper by L. G. Sathe J. Indian Math. Soc, 1954(18):83-87.
[11] Tenenbaum G..Introduction to analytic and probabilistic number theory, Translated from the second French edition(1995)by Thomas C. B.. Cambridge Studies in Advanced Mathematics 46. Cambridge:Cambridge University Press,1995. xvi+448.
[12] Tenenbaum G., Wu J.. Moyennes de certaines fonctions multiplicatives sur les entiers friables.J. reine angew. Math, 2003,564:119-166.

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备注/Memo

备注/Memo:
收稿日期:2017-09-20
基金项目:重庆市教委科学技术研究项目(KJ1601213); 国家自然科学基金(11271249)
作者简介:黄勇庆(1978- )男,四川西充人,中学中级教师,硕士,研究方向:基础数学. 刘双(1987- )女,重庆巫溪县人,讲师,硕士,研究方向:为动力系统.
更新日期/Last Update: 2018-02-25