In 2022, Bergelson and Richter established a new dynamical generalization of the prime number theorem. Later, Loyd showed a disjoint form with the Erdős-Kac theorem. In this talk, we will introduce invariant averages of arithmetic functions under multiplications. Using the properties of invariant averages, we will establish some ergodic theorems over squarefree numbers, which are related to Erdős-Kac Theorem, Bergelson-Richter Theorem and Loyd Theorem. Moreover, we will introduce several variants of Bergelson and Richter's theorem related to integers of power-free polynomial values and some other arithmetic functions.

王标，四川仁寿人，2011年四川大学本科毕业，2014年中国科学院数学研究所硕士毕业，2021年纽约州立大学布法罗分校博士毕业，现为云南大学数学与统计学院副教授。现主持国自然地区基金一项。主要研究方向为解析数论，在J. Number Theory等期刊上已发表论文数篇。