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

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Let Γ ⊂ ℝd be a bounded strictly convex surface. We prove that the number kn(Γ) of points of Γ that lie on the lattice \(\frac{1}{n}\mathbb{Z}^2 \) satisfies the following estimates: lim inf kn(Γ)/nd−2 < ∞ for d ≥ 3 and lim inf kn(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles.

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  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    F. V. Petrov

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  1. F. V. Petrov
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Correspondence to F. V. Petrov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189.

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Petrov, F.V. Estimates for the number of rational points on convex curves and surfaces. J Math Sci 147, 7218–7226 (2007). https://doi.org/10.1007/s10958-007-0538-y

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  • DOI: https://doi.org/10.1007/s10958-007-0538-y

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