Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298570249> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W4298570249 abstract "The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to the 1920s with the theorems of Jarnik and Besicovitch regarding well-approximable and badly-approximable points. In this paper we consider three inhomogeneous problems that further develop these classical results. Firstly, we obtain a Jarnik type theorem for the set of multiplicatively approximable points in the plane. This Hausdorff measure statement does not reduce to Gallagher's Lebesgue measure statement as one might expect and is new even in the homogeneous setting. Next, we establish a Jarnik type theorem for the set of multiplicatively approximable points on a non-degenerate planar curve. This completes the Hausdorff theory for planar curves. Finally, we show that the set of simultaneously inhomogeneously (i,j)-badly approximable points in the plane is of full dimension. The underlying philosophy behind the proof has other applications; e.g. towards establishing the inhomogeneous version of Schmidt's Conjecture. The higher dimensional analogues of the planar results are also discussed." @default.
- W4298570249 created "2022-10-02" @default.
- W4298570249 creator A5056236258 @default.
- W4298570249 creator A5081783143 @default.
- W4298570249 date "2013-09-10" @default.
- W4298570249 modified "2023-09-27" @default.
- W4298570249 title "A note on three problems in metric Diophantine approximation" @default.
- W4298570249 doi "https://doi.org/10.48550/arxiv.1309.2414" @default.
- W4298570249 hasPublicationYear "2013" @default.
- W4298570249 type Work @default.
- W4298570249 citedByCount "0" @default.
- W4298570249 crossrefType "posted-content" @default.
- W4298570249 hasAuthorship W4298570249A5056236258 @default.
- W4298570249 hasAuthorship W4298570249A5081783143 @default.
- W4298570249 hasBestOaLocation W42985702491 @default.
- W4298570249 hasConcept C102966492 @default.
- W4298570249 hasConcept C118615104 @default.
- W4298570249 hasConcept C124101348 @default.
- W4298570249 hasConcept C14158598 @default.
- W4298570249 hasConcept C162324750 @default.
- W4298570249 hasConcept C176217482 @default.
- W4298570249 hasConcept C17744445 @default.
- W4298570249 hasConcept C18903297 @default.
- W4298570249 hasConcept C194198291 @default.
- W4298570249 hasConcept C199539241 @default.
- W4298570249 hasConcept C202444582 @default.
- W4298570249 hasConcept C206530611 @default.
- W4298570249 hasConcept C21547014 @default.
- W4298570249 hasConcept C2777026412 @default.
- W4298570249 hasConcept C2777105136 @default.
- W4298570249 hasConcept C2777299769 @default.
- W4298570249 hasConcept C2780009758 @default.
- W4298570249 hasConcept C2780990831 @default.
- W4298570249 hasConcept C33676613 @default.
- W4298570249 hasConcept C33923547 @default.
- W4298570249 hasConcept C41008148 @default.
- W4298570249 hasConcept C73225184 @default.
- W4298570249 hasConcept C77088390 @default.
- W4298570249 hasConcept C86803240 @default.
- W4298570249 hasConcept C87117476 @default.
- W4298570249 hasConceptScore W4298570249C102966492 @default.
- W4298570249 hasConceptScore W4298570249C118615104 @default.
- W4298570249 hasConceptScore W4298570249C124101348 @default.
- W4298570249 hasConceptScore W4298570249C14158598 @default.
- W4298570249 hasConceptScore W4298570249C162324750 @default.
- W4298570249 hasConceptScore W4298570249C176217482 @default.
- W4298570249 hasConceptScore W4298570249C17744445 @default.
- W4298570249 hasConceptScore W4298570249C18903297 @default.
- W4298570249 hasConceptScore W4298570249C194198291 @default.
- W4298570249 hasConceptScore W4298570249C199539241 @default.
- W4298570249 hasConceptScore W4298570249C202444582 @default.
- W4298570249 hasConceptScore W4298570249C206530611 @default.
- W4298570249 hasConceptScore W4298570249C21547014 @default.
- W4298570249 hasConceptScore W4298570249C2777026412 @default.
- W4298570249 hasConceptScore W4298570249C2777105136 @default.
- W4298570249 hasConceptScore W4298570249C2777299769 @default.
- W4298570249 hasConceptScore W4298570249C2780009758 @default.
- W4298570249 hasConceptScore W4298570249C2780990831 @default.
- W4298570249 hasConceptScore W4298570249C33676613 @default.
- W4298570249 hasConceptScore W4298570249C33923547 @default.
- W4298570249 hasConceptScore W4298570249C41008148 @default.
- W4298570249 hasConceptScore W4298570249C73225184 @default.
- W4298570249 hasConceptScore W4298570249C77088390 @default.
- W4298570249 hasConceptScore W4298570249C86803240 @default.
- W4298570249 hasConceptScore W4298570249C87117476 @default.
- W4298570249 hasLocation W42985702491 @default.
- W4298570249 hasLocation W42985702492 @default.
- W4298570249 hasLocation W42985702493 @default.
- W4298570249 hasOpenAccess W4298570249 @default.
- W4298570249 hasPrimaryLocation W42985702491 @default.
- W4298570249 hasRelatedWork W1786146118 @default.
- W4298570249 hasRelatedWork W1982432039 @default.
- W4298570249 hasRelatedWork W1998428946 @default.
- W4298570249 hasRelatedWork W2036685080 @default.
- W4298570249 hasRelatedWork W2113222768 @default.
- W4298570249 hasRelatedWork W2769250775 @default.
- W4298570249 hasRelatedWork W2800636784 @default.
- W4298570249 hasRelatedWork W3105806929 @default.
- W4298570249 hasRelatedWork W4385292110 @default.
- W4298570249 hasRelatedWork W95455986 @default.
- W4298570249 isParatext "false" @default.
- W4298570249 isRetracted "false" @default.
- W4298570249 workType "article" @default.