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Algebraic points on the plane

Abstract

This article gives quantitative estimates for the measure of points (x, y) of a given rectangle admitting the construction of polynomials P(t) with small (with respect to the height of the polynomial) values of P(x) and P(y). Such estimates can be used in the problem of distribution of algebraic points on the plane.

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Correspondence to V. V. Lebed.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 73–80, 2005.

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Lebed, V.V., Bernik, V.I. Algebraic points on the plane. J Math Sci 146, 5680–5685 (2007). https://doi.org/10.1007/s10958-007-0384-y

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Keywords

  • Manifold
  • Simultaneous Approximation
  • Diophantine Approximation
  • Algebraic Point
  • Reducible Polynomial