Inhomogeneous Diophantine approximation on planar curves

Details Inhomogeneous Diophantine approximation on planar curves Inhomogeneous Diophantine approximation on planar curves

2009-03-16

arxiv.org/abs/0903.2817v1

Mathematics

Number Theory

11 pages

Scientific paper

The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann. of Math. (2), 166 (2007), pp. 367-426] and [Invent. Math., 166 (2006), pp. 103-124]. The key lies in obtaining essentially the best possible results regarding the distribution of `shifted' rational points near planar curves.

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