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Estimates for the number of rational points on convex curves and surfaces

Authors:	F V Petrov

Institution:	(1) St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract:	Let Γ ⊂ ℝ^d be a bounded strictly convex surface. We prove that the number k_n(Γ) of points of Γ that lie on the lattice $\frac{1}{n}\mathbb{Z}^2$ satisfies the following estimates: lim inf k_n(Γ)/n^d−2 < ∞ for d ≥ 3 and lim inf k_n(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189.

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