The Selberg-Delange method in short intervals with some applications

被引：11
作者：
Cui, Zhen [1 ]
Lu, Guangshi [2 ]
Wu, Jie [3 ,4 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[3] Yangtze Normal Univ, Sch Math & Stat, Chongqing 200240, Peoples R China
[4] Univ Lorraine, Inst Elie Cartan Lorraine, F-54506 Vandoeuvre Les Nancy, France
来源：
SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 03期
基金：
中国国家自然科学基金;
关键词：
asymptotic results on arithmetic functions; Selberg-Delange method; arithmetic functions; distribution of integers; 11N37;
D O I：
10.1007/s11425-017-9172-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish a quite general mean value result of arithmetic functions over short intervals with the Selberg-Delange method and give some applications. In particular, we generalize Selberg's result on the distribution of integers with a given number of prime factors and Deshouillers-Dress-Tenenbaum's arcsin law on divisors to the short interval case.
引用
收藏
页码：447 / 468
页数：22
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