2025/03/05 by Peterzil, George, Sapire, Guy
#20H10 (Primary) 37D40 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2503.03461
It is a classical result of Dal'Bo that the length spectrum of a non-elementary Fuchsian group is non-arithmetic, namely, it generates a dense additive subgroup of ℝ. In this note we provide an elementary proof of an extension of this theorem: a non-elementary Fuchsian group contains two elements whose lengths are linearly independent over ℚ, reproving a result of Prasad and Rapinchuk.