Year: 2020
Type: preprint
Abstract: For any cofinite Fuchsian group $Γ\subset {\rm PSL}(2, \mathbb{R})$, we show that any set of $N$ points on the hyperbolic surface $Γ\backslash\mathbb{H}^2$ determines $\geq C_Γ \frac{N}{\log N}$ distinct distances for some constant $C_Γ>0$ depending only on $Γ$. In particular, for $Γ$ being any finite index subgroup of ${\rm PSL}(2, \mathbb{Z})$ with $μ=[{\rm PSL}(2, \mathbb{Z}): Γ]0$.
Source: arXiv (Cornell University)
Author: Meng, Xianchang
Institution: University of Göttingen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3047617221