Diophantine approximation on hyperbolic orbifolds

DOI10.1215/S0012-7094-88-05622-0zbMath0653.10022MaRDI QIDQ1107565

Andrew Haas

Publication date: 1988

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Riemann surfacessimple geodesicsMarkov spectrumTeichmüller class

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Structure of modular groups and generalizations; arithmetic groups (11F06) Markov and Lagrange spectra and generalizations (11J06) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (6)

Length spectra of the Hecke triangle groups ⋮ Closed curves and geodesics with two self-intersections on the punctured torus ⋮ CLASSIFYING LOW HEIGHT GEODESICS ON $\Gamma^3 \backslash \mathcal{H}$ ⋮ Parametrizing simple closed geodesy on Γ³\ℋ ⋮ The Markov spectra for Fuchsian groups ⋮ The Geometry of the Hyperelliptic Involution in Genus Two

Cites Work

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• The geometry of Markoff numbers
• Geodesics with bounded intersection number on surfaces are sparsely distributed
• Characterization of simple closed geodesics on Fricke surfaces
• Diophantine approximation on hyperbolic Riemann surfaces
• Length spectra as moduli for hyperbolic surfaces
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• The Modular Surface and Continued Fractions
• Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum
• The Hurwitz Constant and Diophantine Approximation on Hecke Groups
• Minimum of quadratic forms with respect to Fuchsian groups. I.

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