# Inhomogeneous Diophantine approximation on planar curves

Research group:
 Title Inhomogeneous Diophantine approximation on planar curves Publication Type Journal Article Year of Publication 2011 Authors Beresnevich V, Vaughan R, Velani S Refereed Designation Refereed Journal Math. Annalen Volume 349, no. 4 Pagination 929-942 Abstract 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. URL http://arxiv.org/abs/0903.2817 DOI DOI: 10.1007/s00208-010-0548-9 E-print number arXiv:0903.2817