Diophantine approximation in the field \(\mathbb Q(i\sqrt 2)\)

DOI10.1016/j.jnt.2011.04.002zbMath1229.11099OpenAlexW4212790727MaRDI QIDQ555299

Asmus L. Schmidt

Publication date: 22 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.04.002

zbMATH Keywords

continued fraction algorithmapproximation spectrumMarkoff spectrum

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Markov and Lagrange spectra and generalizations (11J06)

Related Items (4)

The Apollonian structure of Bianchi groups ⋮ Intrinsic Diophantine approximation on circles and spheres ⋮ The dynamics of Super-Apollonian continued fractions ⋮ Continued fractions over non-Euclidean imaginary quadratic rings

Cites Work

• Diophantine approximation in the Eisensteinian field
• On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field
• Ergodic theory for complex continued fractions
• Diophantine approximation of complex numbers
• Diophantine approximation in the field \(\mathbb{Q}(i(11^{1/2}))\)
• A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities
• On metrical theory of diophantine approximation over imaginary quadratic field
• DIOPHANTINE APPROXIMATION IN $\mathbf{Q}(\sqrt{-5})$ AND $\mathbf{Q}(\sqrt{-6})$
• Farey Triangles and Farey Quadrangels in the Complex Plane.
• The metrical theory of complex continued fractions
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