Diophantine approximation on planar curves: the convergence theory

By Robert C. Vaughan, Sanju Velani. 2006

105 citations recorded by the source corpus.

The convergence theory for the set of simultaneously ψ-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in [1] and thereby completes the general metric theory for planar curves.

Subfields: Analytical Chemistry, Mathematical Physics, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/81a3221d3db4e367268e68059042847e12dd77a4

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In Analytical Chemistry

In Mathematical Physics

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Citations in the corpus

Rational points near manifolds and metric Diophantine approximation (2009, background): “Huxley’s estimate was the only general result until Vaughan and Velani remarkably removed the θterm from Huxley’s estimate [54].”
Exponents of Diophantine approximation (2006, result): “atement of Theorem 5.10 was proved by Bernik [11] and the second one is a result of Baker and Schmidt [5]. We display an immediate consequence of results by Beresnevich, Dickinson, Vaughan and Velani [10, 79]. Theorem 5.11. The spectrum of λ2 is equal to [1/2,+∞]. More is known than the mere stateme”
Metric Diophantine Approximation : aspects of recent work (2016, background): “5) for planar curves was established in [90] and subsequently strengthened in [29].”