538 citations
- Centre National de la Recherche ScientifiqueFR7 papers
- Maxwell Institute for Mathematical SciencesGB7 papers
- Royal ObservatoryGB7 papers
- UK Astronomy Technology CentreGB7 papers
- Durham UniversityGB6 papers
- Laboratoire de Mathématiques d'OrsayFR4 papers
- Leiden UniversityNL4 papers
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- Université Jean MonnetFR4 papers
- University of BirminghamGB4 papers
- European Southern ObservatoryCL3 papers
- Institut d'Astrophysique de ParisFR3 papers
5 papers · 1 filter
Salem numbers, Pisot numbers, Mahler measure and graphs
James McKee, Chris Smyth
We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbe…
Successive Minima and Best Simultaneous Diophantine Approximations
Iskander Aliev, Martin Henk
We study the problem of best approximations of a vector by rational vectors of a lattice whose common denominator is bounded. To this e…
Diophantine approximation and badly approximable sets
Simon Kristensen, Rebecca Thorn, Sanju Velani
Let (X,d) be a metric space and (Ω, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Ω. Loose…
A quantitative Khintchine-Groshev type theorem over a field of formal series
M. M. Dodson, S. Kristensen, J. Levesley
An asymptotic formula which holds almost everywhere is obtained for the number of solutions to the Diophantine inequalities |qA-p|<ψ(|q|), where A is an n by m matrix (m>1) over th…
A metric theorem for restricted Diophantine approximation in positive characteristic
Simon Kristensen
We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.