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The Ramanujan Journal

, Volume 9, Issue 1–2, pp 25–32 | Cite as

  • Masaaki AMOU
  • Yann Bugeaud
Article

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.

Keywords

roots of a polynomial separating the roots 

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

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References

  1. 1.
    M. Amou, “On Sprindžuk’s classification of transcendental numbers,” J. Reine Angew. Math. 470 (1996), 27–50.Google Scholar
  2. 2.
    M. Amou, “Transcendence measures for almost all numbers,” in Analytic Number Theory, Japanese (Kyoto, 1995), Sʉrikaisekikenkyʉsho Kɵkyʉroku 961 (1996) 112–116.Google Scholar
  3. 3.
    G.V. Chudnovsky, “Contributions to the theory of transcendental numbers,” A. M. S. Surveys and Monographs 19, Providence USA, 1984.Google Scholar
  4. 4.
    G. Diaz, “Une nouvelle propriété d’approximation diophantienne,” C. R. Acad. Sci. Paris 324 (1997) 969–972.Google Scholar
  5. 5.
    G. Diaz et M. Mignotte, “Passage d’une mesure d’approximation à une mesure de transcendance,” C. R. Math. Rep. Acad. Sci. Canada 13 (1991) 131–134.Google Scholar
  6. 6.
    R. Güting, “Polynomials with multiple zeros,” Mathematika 14 (1967) 149–159.Google Scholar
  7. 7.
    M. Laurent and D. Roy, “Criteria of algebraic independence with multiplicities and interpolation determinants,” Trans. Amer. Math. Soc. 351 (1999) 1845–1870.CrossRefGoogle Scholar
  8. 8.
    M. Mignotte, “On the distance between the roots of a polynomial,” Appl. Algebra Engrg. Comm. Comput. 6 (1995) 327–332.Google Scholar
  9. 9.
    V. G. Sprindžuk, “On a classification of transcendental numbers,” Litovsk. Mat. Sb. 2 (1962) 215–219 (en russe).Google Scholar
  10. 10.
    V. G. Sprindžuk, “Mahler’s problem in metric number theory,” American Mathematical Society, Providence, R.I., 1969, vii+192.Google Scholar
  11. 11.
    M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups, Grundlehren der mathematischen Wissenschaft 326, Springer Verlag, Berlin, Heidelberg, New York, 2000.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsGunma UniversityKiryuJapan
  2. 2.Université Louis Pasteur, U. F. R. de mathématiquesStrasbourg CedexFrance

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