Diophantine approximation on planar curves and the distribution of rational points (with an appendix "Sum of two squares near perfect squares" by R.C. Vaughan)

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Rational points near manifolds and metric Diophantine approximation (2009, background): “the main results of this paper. It is also natural to address a similar question within the above conjectures. Recall that the analyticity assumption is not present in the planar curves results – see [7] and [52]. As we mentioned in §2.1, it has been shown that any C(2) non-degenerate 47 planar curv”