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QUANTITATIVE ESTIMATE FOR THE MEASURE OF A SET OF REAL NUMBERS

Part of: Diophantine approximation, transcendental number theory Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  06 July 2021

NATALIA BUDARINA
NATALIA BUDARINA*
Affiliation:
Department of Computing Science and Mathematics, School of Informatics and Creative Arts, Dundalk Institute of Technology, Dublin Road, Dundalk, Republic of Ireland e-mail: natalia.budarina@dkit.ie
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Abstarct

An effective estimate for the measure of the set of real numbers for which the inequality |P(x)|<Q-w for $w > {3 \over 2}n + 1$ has a solution in integral polynomials P of degree n and of height H(P) at most $Q \in {\rm{\mathbb N}}$ is obtained.

MSC classification

Primary: 11J83: Metric theory 11K60: Diophantine approximation
Secondary: 11J68: Approximation to algebraic numbers
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 411 - 433
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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