Markoff forms and primitive words

DOI10.1007/BF01419427zbMath0227.10018OpenAlexW2089545034MaRDI QIDQ2549344

Harvey Cohn

Publication date: 1972

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

Full work available at URL: https://eudml.org/doc/162238

Mathematics Subject Classification ID

Quadratic forms over global rings and fields (11E12) Approximation to algebraic numbers (11J68) General binary quadratic forms (11E16)

Related Items (27)

The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮ Continued fractions and the Markoff tree ⋮ A palindromization map for the free group ⋮ On the generalized Hurwitz equation and the Baragar-Umeda equation ⋮ On palindromes with three or four letters associated to the Markoff spectrum ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Applications of the theory of modular forms to number theory ⋮ Markov and Lagrange spectra (survey of the literature) ⋮ What does a basis of F(a,b) look like? ⋮ Bifix codes and Sturmian words ⋮ Presentations of some classical groups ⋮ More numerical evidence on the uniqueness of Markov Numbers ⋮ Symmetry of topographs of Markoff forms ⋮ The sum of Lagrange numbers ⋮ Dedekind sums and generalizations of the Markov Diophantine equation ⋮ Zu Fragen der Analysis im Zusammenhang mit der Gleichung \(x^2_1+\dots+x^2_n- ax_1\dots x_n=b\) ⋮ Sturmian morphisms, the braid group \(B_4\), Christoffel words and bases of \(F_2\) ⋮ On quadratic numbers and forms, and Markoff theory ⋮ Ternary forms as invariants of Markoff forms and other \(SL_2(\mathbb{Z})\)- bundles ⋮ On Christoffel classes ⋮ Bowditch’s Q-conditions and Minsky’s primitive stability ⋮ Primitive, almost primitive, test, and \(\Delta\)-primitive elements of free algebras with the Nielsen-Schreier property ⋮ Christoffel Words and Markoff Triples: An Algebraic Approach ⋮ The Uniqueness of the Markoff Numbers ⋮ Geometry and Markoff’s spectrum for ℚ(𝕚), I ⋮ CR-structures on Seifert manifolds ⋮ Stallings graphs, algebraic extensions and primitive elements in F₂

Cites Work

• Unnamed Item
• Die Automorphismengruppe der freien Gruppen
• Lectures on modular functions of one complex variable
• The Markoff chain
• Approach to Markoff's minimal forms through modular functions
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus
• On Certain Sets of Elements in a Free Group
• On the Condition of Riemann Integrability

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