FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 6, PAGES 73-80

Algebraic points on the plain

V. V. Lebed
V. I. Bernik

Abstract

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The article contains 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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Last modified: January 13, 2006