J.UCS The Journal of Universal Computer Science pp 603-613 | Cite as
Bounds for Heights of Integer Polynomial Factors
Chapter
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.
Preview
Unable to display preview. Download preview PDF.
References
- 1.A. G. Akritas: Elements of Computer Algebra with Applications, Wiley & Sons (1989).MATHGoogle Scholar
- 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.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.A.-L. Caüchy: Exercices de Mathématiques, 4éme année. De Bure Frères, Paris (1829).Google Scholar
- 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.D. E. Knuth: The Art of Computer Programming, vol. 2, Seminumerical Algorithms, Addison-Wesley (1981).MATHGoogle Scholar
- 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.K. M Ahler: An application of Jensen’s formulae to polynomials. Mathematical 7,98–100(1960).CrossRefGoogle Scholar
- 9.M. Mignotte: An inequality about factors of polynomials, Math. Comp., 28, 1153–1157 (1974).CrossRefMATHMathSciNetGoogle Scholar
- 10.M. Mignotte: Mathematics for Computer Algebra, Springer Verlag (1991).Google Scholar
- 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.W. Specht: Abschätzungen der Wurzeln algebraischer Gleichungen, Math. Z. 52,310–321(1949).CrossRefMathSciNetGoogle Scholar
Copyright information
© Springer Pub. Co. 1996