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Sur la séparation des racines des polynômes et une question de Sprindžuk

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Résumé

Nous établissons une nouvelle minoration de la distance entre deux racines d’un polynôme à coefficients entiers, que nous appliquons à une question de théorie métrique des nombres posée par Sprindžuk.

Abstract

We establish a new lower bound for the distance between two roots of an integer polynomial. We apply it to a question in metric number theory posed by Sprindžuk.

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Authors and Affiliations

  1. Department of Mathematics, Gunma University, Tenjin-cho 1-5-1, Kiryu, 376-8515, Japan

    Masaaki AMOU

  2. Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084, Strasbourg Cedex, France

    Yann Bugeaud

Authors
  1. Masaaki AMOU
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  2. Yann Bugeaud
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Corresponding author

Correspondence to Masaaki AMOU.

Additional information

À Jean-Louis Nicolas, pour ses soixante ans

2000 Mathematics Subject Classification: Primary—11C08

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AMOU, M., Bugeaud, Y. Sur la séparation des racines des polynômes et une question de Sprindžuk. Ramanujan J 9, 25–32 (2005). https://doi.org/10.1007/s11139-005-0822-8

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  • DOI: https://doi.org/10.1007/s11139-005-0822-8

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