Dynamics on the number of prime divisors for additive arithmetic semigroups

doi:10.1016/j.ffa.2022.102029

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	Dynamics on the number of prime divisors for additive arithmetic semigroups
	Wang, Biao
	2022-08-01
发表期刊	FINITE FIELDS AND THEIR APPLICATIONS
ISSN	1071-5797
卷号	81 页码:28
摘要	In 2020, Bergelson and Richter gave a dynamical generalization of the classical Prime Number Theorem, which has been generalized by Loyd in a disjoint form with the ErdosKac Theorem. These generalizations reveal the rich ergodic properties of the number of prime divisors of integers. In this article, we show a new generalization of Bergelson and Richter's Theorem in a disjoint form with the distribution of the largest prime factors of integers. Then following Bergelson and Richter's techniques, we will show the analogues of all of these results for the arithmetic semigroups arising from finite fields as well. (c) 2022 Elsevier Inc. All rights reserved.
关键词	Prime Number Theorem Liouville function Largest prime factors Uniquely ergodic Uniform distribution
DOI	10.1016/j.ffa.2022.102029
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000805452200007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61479
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Biao
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Biao. Dynamics on the number of prime divisors for additive arithmetic semigroups[J]. FINITE FIELDS AND THEIR APPLICATIONS,2022,81:28.
APA	Wang, Biao.(2022).Dynamics on the number of prime divisors for additive arithmetic semigroups.FINITE FIELDS AND THEIR APPLICATIONS,81,28.
MLA	Wang, Biao."Dynamics on the number of prime divisors for additive arithmetic semigroups".FINITE FIELDS AND THEIR APPLICATIONS 81(2022):28.