The sum of Lagrange numbers

DOI10.1090/proc/15527zbMath1483.11139arXiv2008.07659OpenAlexW3135025992MaRDI QIDQ5157813

Brice Loustau, Jonah Gaster

Publication date: 20 October 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07659

zbMATH Keywords

Markov numbersLagrange numbersMarkov uniqueness conjecture

Mathematics Subject Classification ID

Markov and Lagrange spectra and generalizations (11J06) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

• Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space
• The geometry of Markoff numbers
• Diophantine approximation on hyperbolic Riemann surfaces
• Simple geodesics and a series constant over Teichmüller space
• Geometry of Lobachevskii in connection with certain questions of arithmetic
• The modular group action on real \(SL(2)\)-characters of a one-holed torus
• The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms
• Systoles of arithmetic surfaces and Markoff spectrum
• A simple proof of the Markoff conjecture for prime powers
• Markoff forms and primitive words
• Approach to Markoff's minimal forms through modular functions
• Markov's Theorem and 100 Years of the Uniqueness Conjecture
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• On the Number of Markoff Numbers Below a Given Bound
• Geometry of Riemann surfaces based on closed geodesics
• Don't Try to Solve These Problems
• A Proof of McShane's Identity Via Markoff Triples
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus
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