Asymptotic independence of $\Omega (n)$ and $\Omega (n+1)$ along logarithmic averages

Dimitrios Charamaras, Florian K. Richter

Let $\Omega (n)$ denote the number of prime factors of a positive integer $n$ counted with multiplicities. We show that for any bounded functions $a,b:\mathbb{N}\to \mathbb{C}$, $$\f…