Some ergodic theorems over k-full numbers

2024/06/22 by Biao Wang, Wang, Biao
Computer Science · Mathematics · #Analytic Number Theory Research #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.15698

openalex publication_date 2024/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Recently, the author and his coauthors proved some ergodic theorems over squarefree numbers related to these results. In this paper, building on the previous work, we will derive the analogues of Bergelson-Richter's theorem, Erdős-Kac theorem and Loyd's theorem over k-full numbers for any integer k≥2.

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