2 papers
math.NT2024
On the Local-Global Conjecture for Combinatorial Period Lengths of Closed Billiards on the Regular Pentagon
Alex Kontorovich, Xin Zhang
We study the set of combinatorial lengths of asymmetric periodic trajectories on the regular pentagon, proving a density-one version of a conjecture of Davis-Lelievre.
math.NT2024
An asymptotic local-global theorem on heights of some Kleinian group orbits
Xuan Xuan Xiao, Xin Zhang
We use circle method prove an asymptotic local-global theorem on the heights of point orbits of thin subgroups of Bianchi groups in .