Visible Measures along $\Omega (n)$ and Distribution of Horocycle Orbits

Adam Kanigowski, Kaitlyn Loyd

Let $\Omega (n)$ denote the number of prime factors of $n$, counted with multiplicities. We study the set $Ac{c}^{\Omega }(x)$ of weak-${}^{\ast }$ limits of the sequence $\frac{1}{N}\sum_{n\leq N}δ_{T^{Ω…