A localized Jarnik-Besicovitch Theorem

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dc.creatorBarral, Julien
dc.creatorSeuret, Stephane
dc.date2009-03-12
dc.date.accessioned2026-07-07T12:51:56Z
dc.date.available2026-07-07T12:51:56Z
dc.descriptionFundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form $\{x\in \mathbb{R}: δ_x = δ\}$, where $δ\geq 1$ and $δ_x$ is the Diophantine approximation rate of an irrational number $x$. We go beyond the classical results by computing the Hausdorff dimension of the sets $\{x\in\mathbb{R}: δ_x =f(x)\}$, where $f$ is a continuous function. Our theorem applies to the study of the approximation rates by various approximation families. It also applies to functions $f$ which are continuous outside a set of prescribed Hausdorff dimension.
dc.description31 pages, Figures are available on our web sites
dc.identifierhttps://arxiv.org/abs/0903.2215
dc.identifierhttp://arxiv.org/abs/0903.2215
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223146
dc.subjectNumber Theory
dc.subject11JXX, 11K55, 11K60, 28A78
dc.titleA localized Jarnik-Besicovitch Theorem
dc.typetext

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