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On the rate of convergence to zero of the measure of extremal sets in metric theory of transcendental numbers

  • Natalia BudarinaEmail author
Article
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Abstract

We investigate the question on the rate of convergence to zero of the measure of the set \(x\in \mathbb {R}\) for which the inequality \(|P(x)|<Q^{-w}\) for \(w>n\) has a solution in integral polynomials of degree n and height bounded by \(Q\in \mathbb {N}\). In this paper, for the first time, we obtain an effective estimate for this rate of convergence to zero.

Keywords

Metric Diophantine approximation Extremal sets Sprindzuk theorem 

Mathematics Subject Classification

11J83 11K60 11J68 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dundalk Institute of TechnologyDundalkRepublic of Ireland

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