dc.contributor.author Marnat, Antoine dc.contributor.author Moshchevitin, Nikolay dc.date.accessioned 2018-07-09T08:32:22Z dc.date.available 2018-07-09T08:32:22Z dc.date.issued 2018-07-09 dc.identifier.uri http://publications.mfo.de/handle/mfo/1374 dc.description.abstract We provide a lower bound for the ratio between the ordinary and uniform exponents of both simultaneous Diophantine approximation to n real numbers and Diophantine approximation for one linear form in n variables. This question was first considered in the 50’s by V. Jarník who solved the problem for two real numbers and established certain bounds in higher dimension. Recently different authors reconsidered the question, solving the problem in dimension three with different methods. Considering a new concept of parametric geometry of numbers, W. M. Schmidt and L. Summerer conjectured that the optimal lower bound is reached at regular systems. It follows from a remarkable result of D. Roy that this lower bound is then optimal. In the present paper we give a proof of this conjecture by W. M. Schmidt and L. Summerer. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,15 dc.title An Optimal Bound for the Ratio Between Ordinary and Uniform Exponents of Diophantine Approximation en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-15 local.series.id OWP-2018-15 en_US
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