Continued fractions over non-Euclidean imaginary quadratic rings

DOI10.1016/J.JNT.2022.06.004OpenAlexW3149459088WikidataQ114156446 ScholiaQ114156446MaRDI QIDQ2109423

Daniel E. Martin

Publication date: 21 December 2022

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

Full work available at URL: https://arxiv.org/abs/1908.00121

zbMATH Keywords

Diophantine approximationcontinued fractionsEuclideannearest integer algorithmimaginary quadratic

Mathematics Subject Classification ID

Quadratic extensions (11R11) Continued fractions and generalizations (11J70) Continued fractions (11A55) Continued fraction calculations (number-theoretic aspects) (11Y65) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Approximation by numbers from a fixed field (11J17)

Related Items (1)

On the existence of the Legendre constants for some complex continued fraction expansions over imaginary quadratic fields

Cites Work

• Diophantine approximation in the field \(\mathbb Q(i\sqrt 2)\)
• A generalization of continued fractions
• Diophantine approximation in the Eisensteinian field
• Approximation properties of some complex continued fractions
• Diophantine approximation of complex numbers
• Diophantine approximation in the field \(\mathbb{Q}(i(11^{1/2}))\)
• Shrinking the period lengths of continued fractions while still capturing convergents
• Generators and relations for certain special linear groups
• Continued fraction expansions for complex numbers–-a general approach
• Visualizing the Arithmetic of Imaginary Quadratic Fields
• A new class of continued fraction expansions
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