A zero-one law for improvements to Dirichlet’s Theorem
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Publication:4604662
DOI10.1090/proc/13685zbMath1448.11126arXiv1609.06780OpenAlexW2963272136MaRDI QIDQ4604662
Nick Wadleigh, Dmitry Kleinbock
Publication date: 5 March 2018
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1609.06780
Continued fractions and generalizations (11J70) Simultaneous homogeneous approximation, linear forms (11J13) Homogeneous approximation to one number (11J04) Homogeneous flows (37A17)
Related Items (34)
The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers ⋮ A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS ⋮ HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS ⋮ Hausdorff measure of sets of Dirichlet non-improvable affine forms ⋮ On the relative growth rate of the product of consecutive partial quotients in continued fraction expansions of Laurent series ⋮ Shrinking targets for discrete time flows on hyperbolic manifolds ⋮ On the dimension drop conjecture for diagonal flows on the space of lattices ⋮ A note on the relative growth of products of multiple partial quotients in the plane ⋮ The distribution of the large partial quotients in continued fraction expansions ⋮ Exact uniform approximation and Dirichlet spectrum in dimension at least two ⋮ A note on Dirichlet spectrum ⋮ A measure estimate in geometry of numbers and improvements to Dirichlet's theorem ⋮ Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions ⋮ Uniform Diophantine approximation with restricted denominators ⋮ Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ Hausdorff dimension of an exceptional set in the theory of continued fractions ⋮ SET OF EXTREMELY DIRICHLET NON-IMPROVABLE POINTS ⋮ Hausdorff dimension of Dirichlet non-improvable set versus well-approximable set ⋮ Metrical properties for the weighted sums of degrees of multiple partial quotients in continued fractions of Laurent series ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series ⋮ Metrical properties for functions of consecutive multiple partial quotients in continued fractions ⋮ Metric properties of the product of consecutive partial quotients in continued fractions ⋮ Unnamed Item ⋮ The sets of Dirichlet non-improvable numbers versus well-approximable numbers ⋮ Critical loci of convex domains in the plane ⋮ Metrical properties for continued fractions of formal Laurent series ⋮ An inhomogeneous Dirichlet theorem via shrinking targets ⋮ Uniformly non–improvable Dirichlet set via continued fractions ⋮ Dimension theory of the product of partial quotients in Lüroth expansions ⋮ Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions * ⋮ METRICAL PROBLEMS IN DIOPHANTINE APPROXIMATION ⋮ Limit theorems for sums of products of consecutive partial quotients of continued fractions ⋮ HAUSDORFF DIMENSION FOR THE SET OF POINTS CONNECTED WITH THE GENERALIZED JARNÍK–BESICOVITCH SET
Cites Work
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- Dirichlet's theorem on Diophantine approximation and homogeneous flows
- Diophantine approximation
- Logarithm laws for flows on homogeneous spaces
- Some metrical theorems in number theory
- Expanding translates of curves and Dirichlet-Minkowski theorem on linear forms
- Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
- An inhomogeneous Dirichlet theorem via shrinking targets
- Dirichlet's theorem on diophantine approximation. II
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