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Polynômes à coefficients positifs multiples d'un polynôme donné

Part of the Lecture Notes in Mathematics book series (LNM,volume 1415)

Abstract

For a given polynômial P with real coefficients, does there exist an other polynômial Q suth that the product PQ has only positive coefficients, and what can be said about the minimal value of the degree of such a polynômial Q? Some general answers are given, and some more precise results are obtained for polynômials P of a particular form: in this case, the estimates of the lowest degree of Q is of interest to study some normal sets, in the uniform distribution theory.

Keywords

  • Acta Arith
  • Positif Multiple
  • Strictement Positif
  • Exemple Simple
  • Sont Donc

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographie

  1. BOREL J-P. Suites de longueur minimale associées à un ensemble normal donné, Israel J. of Math. 64 (1989), à paraître.

    Google Scholar 

  2. BOREL J-P. Parties d'ensembles b-normaux, Manuscripta Math. 62 (1988), p. 317–335.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. DRESS F. et MENDES-FRANCE M. Caractérisation des ensembles normaux dans Z, Acta Arith. 17 (1970), p. 115–120.

    MathSciNet  MATH  Google Scholar 

  4. ERDÖS P. Note on sequences of integers no one of which is divisible by any other, J. London Math. Soc. 10 (1935), p. 126–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. GROSSWALD E. Reductible rational fractions of the type of Gaussian polynômials with only non negative coefficients, Canad. Math. Bull. 21 (1978), p. 21–30.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. HALBERSTAM H. et ROTH K.F. “Sequences”, Oxford at the Clarendon Press, 1966.

    Google Scholar 

  7. MEISSNER E. Uber positive Darstellung von Polynomen, Math. Annalen 70 (1911), p. 223–235.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. KUIPERS L. et NIEDERREITER H. Uniform distribution of sequences, Wiley Interscience, New York, 1974.

    MATH  Google Scholar 

  9. RAUZY G. Caractérisation des ensembles normaux, Bull. SMF 98 (1970), p. 401–414.

    MathSciNet  MATH  Google Scholar 

  10. REICH D. On certain polynomials of Gaussian type, Canad. J. Math. 31 no2 (1979), p. 274–281.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. TENENBAUM G. Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné, Compositio Math. 51 (1984), p. 243–263.

    MathSciNet  MATH  Google Scholar 

  12. TENENBAUM G. Un problème de probabilité conditionnelle en Arithmétique, Acta Arith. 49 (1987), p. 165–187.

    MathSciNet  MATH  Google Scholar 

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© 1990 Springer-Verlag

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Borel, JP. (1990). Polynômes à coefficients positifs multiples d'un polynôme donné. In: Langevin, M., Waldschmidt, M. (eds) Cinquante Ans de Polynômes Fifty Years of Polynomials. Lecture Notes in Mathematics, vol 1415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084881

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  • DOI: https://doi.org/10.1007/BFb0084881

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52190-7

  • Online ISBN: 978-3-540-46919-3

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