Alex Kontorovich

collaborators

Showing math.NTShow all

2 papers · 1 filter

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

Lax-Phillips orbit counting in higher rank

Alex Kontorovich, Christopher Lutsko

Given a discrete lattice, $Γ < SL_{m} (R)$ , and a base point $o \in R^{m}$ , let $N_{Γ} (T)$ denote the number of points in the orbit $o \cdot Γ$ whose (Eucl…