Some manifolds of Khinchin type for convergence
David Simmons1
1 University of York Department of Mathematics Heslington, York YO10 5DD, UK
Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 175-193.

Recently, Beresnevich, Vaughan, Velani, and Zorin gave in [2] some sufficient conditions for a manifold to be of Khinchin type for convergence. We show that their techniques can be used in a more optimal way to yield stronger results. In the process we also improve a theorem of Dodson, Rynne, and Vickers [5].

Récemment, Beresnevich, Vaughan, Velani et Zorin [2] ont donné des conditions suffisantes pour qu’une variété soit de type Khinchin pour la convergence. Nous montrons que leurs techniques peuvent être utilisées de manière plus optimale pour obtenir des résultats plus solides. Dans le processus, nous améliorons également un théorème de Dodson, Rynne et Vickers [5].

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1021
Classification: 11J13, 11J83, 11L07
Keywords: Diophantine approximation, Khinchin type for convergence, Hausdorff dimension, rational points near manifolds
David Simmons 1

1 University of York Department of Mathematics Heslington, York YO10 5DD, UK
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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David Simmons. Some manifolds of Khinchin type for convergence. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 175-193. doi : 10.5802/jtnb.1021. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1021/

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