上海交通大学学报

上海交通大学学报 >

2017 , Vol. 51 >Issue 11: 1405 - 1408

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2017.11.018

兵器工业

一类数的分解在算术级数中的分布

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  • 1. 长江师范学院 数学与统计学院, 重庆 408100； 2. 上海交通大学 数学科学学院, 上海 200240； 3. 重庆工业职业技术学院 基础教学部, 重庆 401120

网络出版日期: 2017-11-30

基金资助

国家自然科学基金(11271249)，重庆市教委科研项目(KJ1601213)，长江师范学院科研资助项目(2017KYQD102;2012XJYBO31)

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The Distribution for Some Certain Factorizations of the Natural Number in Arithmetic Progressions

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  • 1. College of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, China; 2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China; 3. Department of Basic Courses, Chongqing Industry Polytechnical College, Chongqing 401120, China

Online published: 2017-11-30

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摘要

研究了一类数的分解在算术级数中的分布问题，利用Selberg-Delange方法和Perron公式得到了一个精确的渐近公式，该结果是无条件的.

关键词： Selberg-Delange方法; 算术级数; Perron 公式

本文引用格式

冯彬1,2,刘双3 . 一类数的分解在算术级数中的分布[J]. 上海交通大学学报, 2017 , 51(11) : 1405 -1408 . DOI: 10.16183/j.cnki.jsjtu.2017.11.018

Abstract

The distribution for some certain factorizations of the natural number in arithmetic progressions was studied and an asymptotic formula was obtained by Selberg-Delange method and Perron’s formula. The formula is unconditional.

Key words： Selberg-Delange method; arithmetic progressions; Perron’s formula

参考文献

［1］CANFIELD E R, ERDS P, POMERANCE C. On a problem of Oppenheim concerning “factorisatio numerorum”［J］. J Number Theory, 1983, 17(1): 1-28. ［2］LUCA F, MUKHOPADHYAY A, SRINIVAS K. Some results on Oppenheim’s “factorisatio numerorum” function［J］. Acta Arith, 2010, 142(1): 41-50. ［3］TENENBAUM G. Introduction to analytic and probabilistic number theory ［M］. Cambridge: Cambridge University Press, 1995. ［4］CUI Z, WU J. The Selberg-Delange method in short intervals with an application［J］. Acta Arith, 2014, 163(3): 247-260. ［5］FENG B. On the arcsine law on divisors in arithmetic progressions［J］. Indagationes Mathematicae, 2016, 27(3): 749-763. ［6］FENG B, CUI ZHEN. DDT theorem over square-free numbers in short interval［J］. Front Math China, 2017, 12(2): 367-375. ［7］PAN C D, PAN C B. Fundamentals of analytic number theory ［M］. Beijing: Science Press, 1991.
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