Diophantine approximation on planar curves: the convergence theory

Details Diophantine approximation on planar curves: the convergence theory Diophantine approximation on planar curves: the convergence theory

2006-02-10

arxiv.org/abs/math/0602225v1

Mathematics

Number Theory

18 pages. To appear in Invent. Math

Scientific paper

10.1007/s00222-006-0509-9

The convergence theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in `Diophantine approximation on planar curves and the distribution of rational points' (by V. Beresnevich, H. Dickinson, and S. Velani, with an Appendix: `Sums of two squares near perfect squares' by R.C. Vaughan, To appear: Annals of Math., Pre-print: arkiv:math.NT/0401148, (2004), 1-52.) and thereby completes the general metric theory for planar curves.

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