Dynamics on the number of prime divisors for additive arithmetic semigroups

讲座时间 Datetime: 2021年11月22日，星期一，9:00-10:30

地点 Venue: 腾讯会议，813 107 216

报告人 Speaker:  王标 博士

单位 Affiliation: 中国科学院数学与系统科学研究院华罗庚中心

报告摘要 Abstract:

In 2020, Bergelson and Richter gave a dynamical generalization of the classical Prime Number Theorem, which is generalized by Loyd in a disjoint form with the Erdős-Kac Theorem recently. These generalizations reveal the rich ergodic properties of the number of prime divisors of integers. In this talk, we will show a new generalization of Bergelson and Richter's Theorem in a disjoint form with the distribution of the largest prime factors of integers. And 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.