Cubic irrationals and periodicity via a family of multi-dimensional continued fraction algorithms

DOI10.1007/s00605-014-0643-1zbMath1305.11060arXiv1208.4244OpenAlexW2063780073MaRDI QIDQ403823

Krishna Dasaratha, Chansoo Lee, Thomas Garrity, Matthew Stoffregen, Nicholas Neumann-Chun, Cornelia Mihaila, Sarah Peluse, Laure Flapan

Publication date: 29 August 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4244

zbMATH Keywords

multidimensional continued fractionscubic number fieldsHermite problem

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Continued fractions (11A55)

Related Items (6)

Lagrange's theorem for continued fractions on the Heisenberg group ⋮ On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups ⋮ Linear recurrence sequences and periodicity of multidimensional continued fractions ⋮ Simultaneous approximations to \(p\)-adic numbers and algebraic dependence via multidimensional continued fractions ⋮ Generalizing the Minkowski question mark function to a family of multidimensional continued fractions ⋮ On the periodic writing of cubic irrationals and a generalization of Rédei functions

Cites Work

• The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
• Ergodic properties of triangle partitions
• A generalized family of multidimensional continued fractions: TRIP Maps
• On the Computation of Totally Real Quartic Fields of Small Discriminant
• Geometry of continued fractions
• On periodic sequences for algebraic numbers
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