Đề tài " Diophantine approximation on planar curves and the distribution of rational points "

Sums of two squares near perfect squares by R. C. Vaughan∗∗∗ In memory of Pritish Limani (1983–2003) Abstract Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type for divergence; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on C of C(ψ) is full. We also obtain the Hausdorff measure analogue of the divergent Khintchine type result. ...