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Diophantine approximation on planar curves: the convergence theory

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Abstract

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.

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References

  1. Beresnevich, V., Dickinson, H., Velani, S.: Diophantine approximation on planar curves and the distribution of rational points, with an Appendix, Sums of two squares near perfect squares by R.C. Vaughan. To appear in Ann. Math., preprint: arkiv:math.NT/0401148, 1–52 (2004)

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Authors and Affiliations

  1. Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA, 16802-6401, USA

    R.C. Vaughan

  2. Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

    S. Velani

Authors
  1. R.C. Vaughan
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  2. S. Velani
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Corresponding author

Correspondence to R.C. Vaughan.

Additional information

Dedicated to Walter Hayman and Klaus Roth on their eightieth birthdays

Mathematics Subject Classification (2000)

11J83; 11J13, 11K60

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Vaughan, R., Velani, S. Diophantine approximation on planar curves: the convergence theory. Invent. math. 166, 103–124 (2006). https://doi.org/10.1007/s00222-006-0509-9

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  • DOI: https://doi.org/10.1007/s00222-006-0509-9

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