Sparse Equidistribution of Unipotent Orbits in Finite-Volume Quotients of $\text{PSL}(2,\mathbb{R})$, with appendices

Cheng Zheng

In this note, we consider the orbits $\{pu(n^{1+\gamma })|n\in \mathbb{N}\}$ in $\Gamma \backslash \text{PSL}(2,\mathbb{R})$, where $\Gamma$ is a non-uniform lattice in $\text{PSL}(2,\mathbb{R})$ and $u…