Systoles of arithmetic surfaces and Markoff spectrum

DOI10.1007/BF01444218zbMath0853.11054OpenAlexW1989764769MaRDI QIDQ1914737

Paul Schmutz Schaller

Publication date: 9 July 1996

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165440

zbMATH Keywords

geodesicssystolesMarkoff spectrumMarkoff numbersprincipal congruence covers

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Structure of modular groups and generalizations; arithmetic groups (11F06) Markov and Lagrange spectra and generalizations (11J06) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Minima of forms (11H50)

Related Items

The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms, Continued fractions and the Markoff tree, Generalization of Markov Diophantine equation via generalized cluster algebra, On the Frobenius conjecture for Markoff numbers, Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space, A simple proof of the Markoff conjecture for prime powers, The sum of Lagrange numbers, Markoff numbers and ambiguous classes, The modular torus has maximal length spectrum, Geometry and Markoff’s spectrum for ℚ(𝕚), I

Cites Work

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• Diophantine approximation on hyperbolic Riemann surfaces
• Integral solutions of Markoff-Hurwitz equations
• Arithmetic Fuchsian groups and the number of systoles
• Approach to Markoff's minimal forms through modular functions
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• Observables of a Dirac Particle
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus