An inequality about factors of polynomials

Author:
M. Mignotte

Journal:
Math. Comp. **28** (1974), 1153-1157

MSC:
Primary 12D05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0354624-3

MathSciNet review:
0354624

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Abstract | References | Similar Articles | Additional Information

Abstract: A sharp inequality is proved about the product of some roots of a polynomial. It is used to bound the height of the factors of a polynomial. Applications are given to the problem of factorization and numerical examples show that these bounds strongly improve the previous ones.

**[1]**K. MAHLER, "An application of Jensen's formula to polynomials,"*Mathematika*, v. 7, 1960, pp. 98-100. MR**23**#A1779. MR**0124467 (23:A1779)****[2]**M. MIGNOTTE, "Critères d'irréducibilité des polynomes sur un corps de nombres,"*Enseignement Math.*, v. 18, 1972, pp. 191-200. MR**0347770 (50:271)****[3]**H. ZASSENHAUS, "On Hensel factorization. I,"*J. Number Theory*, v. 1, 1969, pp. 291-311. MR**39**#4120. MR**0242793 (39:4120)****[4]**H. G. ZIMMER,*Computational Problems, Methods and Results in Algebraic Number Theory*, Lecture Notes in Math., vol. 269, Springer-Verlag, Berlin, 1972. MR**0323751 (48:2107)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0354624-3

Keywords:
Inequality,
roots of polynomial,
factorization

Article copyright:
© Copyright 1974
American Mathematical Society