The Markoff equation \(X^ 2+Y^ 2+Z^ 2=aXYZ\) over quadratic imaginary fields

DOI10.1016/0022-314X(90)90105-ZzbMath0702.11012MaRDI QIDQ914725

Joseph H. Silverman

Publication date: 1990

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

zbMATH Keywords

ordersasymptotic formulaimaginary quadratic fieldMarkov equation

Mathematics Subject Classification ID

Cubic and quartic Diophantine equations (11D25)

Related Items (15)

Arithmetic hyperbolic surface bundles ⋮ On the generalized Hurwitz equation and the Baragar-Umeda equation ⋮ On the diophantine equations generalizing those of Markoff ⋮ Rational points on \(K3\) surfaces in \(\mathbb{P}^ 1\times\mathbb{P}^ 1\times\mathbb{P}^ 1\) ⋮ The equation \(ax^2+by^2+cz^2=dxyz\) over quadratic imaginary fields ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Nonlinear descent on moduli of local systems ⋮ Markoff-Rosenberger triples with Fibonacci components ⋮ Generalized Markoff maps and McShane's identity ⋮ The Markoff equation over polynomial rings ⋮ ON MARKOFF–HURWITZ EQUATIONS OVER RESIDUE CLASS RINGS ⋮ Unnamed Item ⋮ The Markoff-Hurwitz equations over number fields ⋮ Generalizations of the Markoff–Hurwitz equations over residue class rings ⋮ Commutators in $SL_2$ and Markoff surfaces I

Cites Work

• On the Number of Markoff Numbers Below a Given Bound
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