Multifractal analysis of the cusp winding spectrum for Fuchsian groups of the first kind
Volume 224 / 2026
Acta Arithmetica 224 (2026), 271-286
MSC: Primary 37D35; Secondary 37D25, 37E05, 11A55, 11K50
DOI: 10.4064/aa251223-1-5
Published online: 20 July 2026
Abstract
We study the cusp winding process of the geodesic flow on a hyperbolic surface with cusps, uniformised by a finitely generated Fuchsian group of the first kind. We establish the exact exponential asymptotics of the cusp winding spectrum at infinity, extending a result of Cesaratto and Vallée for continued fractions.
