The worst approximable rational numbers

DOI10.1016/j.jnt.2024.04.013MaRDI QIDQ6585660

Boris A. Springborn

Publication date: 12 August 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Diophantine approximationMarkov equationapproximation constantmodular torus

Mathematics Subject Classification ID

Teichmüller theory for Riemann surfaces (30F60) Markov and Lagrange spectra and generalizations (11J06)

Cites Work

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• Decorated Teichmüller theory
• Simple geodesics on a punctured surface
• McShane's identity, using elliptic elements
• Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space
• The geometry of Markoff numbers
• Diophantine approximation on hyperbolic Riemann surfaces
• Euclidean decompositions of noncompact hyperbolic manifolds
• The decorated Teichmüller space of punctured surfaces
• Simple geodesics and a series constant over Teichmüller space
• The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms
• Systoles of arithmetic surfaces and Markoff spectrum
• Discrete conformal maps and ideal hyperbolic polyhedra
• Approach to Markoff's minimal forms through modular functions
• Markov's Theorem and 100 Years of the Uniqueness Conjecture
• On the Number of Markoff Numbers Below a Given Bound
• On the minimum of zero indefinite binary quadratic forms
• WEIERSTRASS POINTS AND SIMPLE GEODESICS
• From Christoffel Words to Markoff Numbers
• A Proof of McShane's Identity Via Markoff Triples
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus
• Ergodic Theory

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