Work

Some ergodic theorems over squarefree numbers and squarefull numbers

Year: 2025

Type: article

Abstract: In 2022, Bergelson and Richter gave a new dynamical generalization of the prime number theorem by establishing an ergodic theorem along the number of prime factors of integers. They also showed that this generalization holds as well if the integers are restricted to be squarefree. In this paper, we present the concept of invariant averages under multiplications for arithmetic functions. Utilizing the properties of these invariant averages, we derive several ergodic theorems over squarefree numbers and squarefull numbers. These theorems have significant connections with the Erdős–Kac theorem, the Bergelson–Richter theorem, and the Loyd theorem.

Source: Acta Arithmetica

DOI: 10.4064/aa240909-18-6

Authors: Huixi Li, Biao Wang, Chunlin Wang, Shaoyun Yi

Institutions: Nankai University, Yunnan University, Sichuan Normal University, Xiamen University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G3879416285, G6733207420, G7043329736, G7526303058