Bounds for Heights of Integer Polynomial Factors

  • Laurenţiu Panaitopol
  • Doru Ştefănescu

Abstract

We describe new methods for the estimation of the bounds of the coefficients of proper divisors of integer polynomials in one variable. There exist classes of polynomials for which our estimates are better than those obtained using the polynomial measure or the 2-weighted norm.

Keywords

Unit Disk Complex Polynomial Real Polynomial Sharp Result Polynomial Factor 
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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References

  1. 1.
    A. G. Akritas: Elements of Computer Algebra with Applications, Wiley & Sons (1989).MATHGoogle Scholar
  2. 2.
    B. Beauzamy, E. Bombieri, P. Enflo, H. Montgomery: Products of poly-nomials in many variables, J. Number Theory, 36, 219–245 (1990).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    B. Beauzamy: Products of polynomials and a priori estimates for coefficients in polynomial decompositions: A sharp result, J. Symb. Comp. 13, 463–472 (1992).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    A.-L. Caüchy: Exercices de Mathématiques, 4éme année. De Bure Frères, Paris (1829).Google Scholar
  5. 5.
    G. Eneström: Händelning af en allmän formel för antalet pensionärer, som vid en tidpuiikt förefinns inom en sluten pension kassa, Öfversigt af velinskaps- akademiens förhandlinger (Stockholm) 50, 405–415 (1893).Google Scholar
  6. 6.
    D. E. Knuth: The Art of Computer Programming, vol. 2, Seminumerical Algorithms, Addison-Wesley (1981).MATHGoogle Scholar
  7. 7.
    E. Landau: Sur quelques théorèmes de M. Petrovitch relatifs aux zéros des fonctions algébriques, Bull. Soc. Math. France, 33, 251–261 (1905).MATHMathSciNetGoogle Scholar
  8. 8.
    K. M Ahler: An application of Jensen’s formulae to polynomials. Mathematical 7,98–100(1960).CrossRefGoogle Scholar
  9. 9.
    M. Mignotte: An inequality about factors of polynomials, Math. Comp., 28, 1153–1157 (1974).CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    M. Mignotte: Mathematics for Computer Algebra, Springer Verlag (1991).Google Scholar
  11. 11.
    L. Panaitopol, D. ŞTefănescu: Some polynomial factorizations over the integers, Bull. Math. Soc. Sc. Math. Roumanie, 37 (85), n. 3–4 (1993). [to appear]Google Scholar
  12. 12.
    W. Specht: Abschätzungen der Wurzeln algebraischer Gleichungen, Math. Z. 52,310–321(1949).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Pub. Co. 1996

Authors and Affiliations

  • Laurenţiu Panaitopol
    • 1
  • Doru Ştefănescu
    • 2
  1. 1.Faculty of MathematicsUniversity of BucharestBucarestRomania
  2. 2.Faculty of Physics, Department of MathematicsUniversity of BucharestBucharest 39Romania

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