Generalizations of the Erds-Kac Theorem and the Prime Number Theorem

被引：0

作者：

Wang, Biao ^{[1
]}

Wei, Zhining ^{[2
]}

Yan, Pan ^{[3
]}

Yi, Shaoyun ^{[4
]}

机构：

[1] Chinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[3] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2023年

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Erds-Kac Theorem; Erds-Pomerance Theorem; Largest prime factor; Prime Number Theorem; 11K36; 37A44; MULTIPLICATIVE FUNCTIONS; SUMS;

D O I：

10.1007/s40304-023-00354-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers. Under a restriction on the largest prime factors of integers, we will refine the Erds-Kac Theorem and Loyd's recent result on Bergelson and Richter's dynamical generalizations of the Prime Number Theorem, respectively. At the end, we will show that the analogue of these results holds with respect to the Erds-Pomerance Theorem as well.

引用

页数：21

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