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On the Distance Between Two Algebraic Numbers

  • Artūras DubickasEmail author
Article
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Abstract

In this paper we give an estimate for the difference between the moduli of two roots of a polynomial with integer coefficients in terms of its degree and Mahler measure. An application of this estimate implies a stronger version of a recent result of Gómez Ruiz and Luca. In passing, we prove an estimate for the distance between two algebraic numbers in terms of their degrees and Mahler measures. For possible applications all our results are given with explicit constants. They are stated without any extra conditions or unnecessary assumptions whenever possible.

Keywords

Polynomial root separation Mahler measure Confluent Vandermonde determinant 

Mathematics Subject Classification

11C08 11R09 12D10 

Notes

Acknowledgements

I thank both referees for pointing out some small errors, misprints, bad notation, misspelled names, etc. This research was funded by the European Social Fund according to the activity ‘Improvement of researchers’ qualification by implementing world-class R&D projects’ of Measure No. 09.3.3-LMT-K-712-01-0037.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Faculty of MathematicsVilnius UniversityVilniusLithuania

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