On well-approximable matrices over a field of formal series

DOI10.1017/S0305004103006911zbMath1088.11056OpenAlexW2028830339MaRDI QIDQ4461537

Simon Kristensen

Publication date: 18 May 2004

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004103006911

zbMATH Keywords

Hausdorff dimensionHaar measureubiquitous systemfield of formal power serieswell-approximable matrix

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory (11J83) Approximation in non-Archimedean valuations (11J61)

Related Items (22)

Invariance principles for Diophantine approximation of formal Laurent series over a finite base field ⋮ Khintchine's theorem for affine hyperplanes in positive charateristic ⋮ Hausdorff dimensions of bounded-type continued fraction sets of Laurent series ⋮ Badly approximable systems of linear forms over a field of formal series ⋮ An extension of the Khinchin–Groshev theorem ⋮ Metric Diophantine approximation over a local field of positive characteristic ⋮ On the relative growth rate of the product of consecutive partial quotients in continued fraction expansions of Laurent series ⋮ Diophantine approximation and beta-expansions over the field of formal Laurent series ⋮ Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series ⋮ Measure theoretic laws for limsup sets defined by rectangles ⋮ Inhomogeneous Diophantine approximation over the field of formal Laurent series ⋮ Cantor sets determined by partial quotients of continued fractions of Laurent series ⋮ A note on badly approximable systems of linear forms over a field of formal series ⋮ Metrical properties for the weighted sums of degrees of multiple partial quotients in continued fractions of Laurent series ⋮ On sets of exact Diophantine approximation over the field of formal series ⋮ On sums of degrees of the partial quotients in continued fraction expansions of Laurent series ⋮ Ultrametric logarithm laws. II ⋮ Metrical properties for continued fractions of formal Laurent series ⋮ On homogeneous and inhomogeneous Diophantine approximation over the fields of formal power series ⋮ ON THE LARGEST DEGREE OF THE PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS OVER THE FIELD OF FORMAL LAURENT SERIES ⋮ A quantitative Khintchine-Groshev type theorem over a field of formal series ⋮ Diophantine approximation in Banach spaces

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