Abstract
AbstractThis paper develops the metric theory of simultaneous inhomogeneous Diophantine approximation on a planar curve with respect to multiple approximating functions. Our results naturally generalize the homogeneous Lebesgue measure and Hausdorff dimension results for the sets of simultaneously well-approximable points on planar curves, established in Badziahin and Levesley (Glasg. Math. J., 49(2):367–375, 2007), Beresnevich et al. (Ann. of Math. (2), 166(2):367–426, 2007), Beresnevich and Velani (Math. Ann., 337(4):769–796, 2007) and Vaughan and Velani (Invent. Math., 166(1):103–124, 2006).
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