2024/12/05 by Xiao, Rongzhong
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2412.03852
In this paper, we build some ergodic theorems involving function Ω, where Ω(n) denotes the number of prime factors of a natural number n counted with multiplicities. As a combinatorial application, it is shown that for any k∈ ℕ and every A⊂ ℕ with positive upper Banach density, there are a,d∈ ℕ such that a,a+d,…,a+kd,a+Ω(d)∈ A.