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On Integer Polynomials with Multiple Roots

Part of: Polynomials and matrices

Published online by Cambridge University Press:  21 December 2009

Masaaki Amou  and
Yann Bugeaud
Masaaki Amou
Affiliation:
Department of Mathematics, Gunma University, Tenjin-cho 1–5–1, Kiryu 376–8515, Japan. E-mail: amou@math.sci.gunma-u.ac.jp
Yann Bugeaud
Affiliation:
Université Louis Pasteur, Mathématiques, 7, rue René Descartes, 67084 Strasbourg Cedex, France. E-mail: bugeaud@math.u-strasbg.fr
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Abstract

A new lower bound is established for the distance between two roots of an integer polynomial, and a new upper bound for the distance between a given real number and the set of zeros of an integer polynomial. The latter result is applied to improve a metrical result in Diophantine approximation.

MSC classification

Secondary: 11C08: Polynomials
Type
Research Article
Information
Mathematika , Volume 54 , Issue 1-2 , December 2007 , pp. 83 - 92
Copyright
Copyright © University College London 2007

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References

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