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Bounds for the multiplicities of the roots of a complex polynomial

  • A. I. Bonciocat (a1), N. C. Bonciocat (a1) and A. Zaharescu (a2)

Abstract

We refine a result of Dubickas on the maximal multiplicity of the roots of a complex polynomial, and obtain several separability criteria for complex polynomials with large leading coefficient. We also give p-adic analogous results for polynomials with integer coefficients.

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1.Alkan, E., Bonciocat, A. I., Bonciocat, N. C. and Zaharescu, A., Square-free criteria for polynomials using no derivatives, Proc. Am. Math. Soc. 135(3) (2007), 677687.
2.Ballieu, R., Sur les limitations des racines d'une équation algébrique, Acad. R. Belg. Bull. Class. Sci. 33(5) (1947), 747750.
3.Bonciocat, A. I. and Bonciocat, N. C., On the irreducibility of polynomials with leading coefficient divisible by a large prime power, Am. Math. Mon. 116(8) (2009), 743745.
4.Bonciocat, A. I. and Bonciocat, N. C., The irreducibility of polynomials that have one large coefficient and take a prime value, Can. Math. Bull. 52(4) (2009), 511520.
5.Bonciocat, A. I., Bonciocat, N. C. and Zaharescu, A., Bounds for the multiplicities of the roots for some classes of complex polynomials, Math. Inequal. Applic. 9(1) (2006), 1122.
6.Dubickas, A., An inequality for the multiplicity of the roots of a polynomial, in Number theory and polynomials, London Mathematical Society Lecture Note Series, Volume 352, pp. 121126 (Cambridge University Press, 2008).
7.Kostrikin, A. I., Introduction to algebra (Springer, 1982).
8.Lang, S., Algebra, Graduate Texts in Mathematics, Volume 211 (Springer, 2002).
9.Marden, M., Geometry of polynomials, Mathematical Surveys and Monographs, Volume 3 (American Mathematical Society, Providence, RI, 1989).
10.Perron, O., Algebra, II: Theorie der algebraischen Gleichungen (de Gruyter, Berlin, 1951).
11.Waldschmidt, M., Diophantine approximation on linear algebraic groups: transcendence properties of the exponential function in several variables (Springer, 2000).
12.Walker, R. J., Algebraic curves (Princeton University Press, 1950).

Keywords

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Bounds for the multiplicities of the roots of a complex polynomial

  • A. I. Bonciocat (a1), N. C. Bonciocat (a1) and A. Zaharescu (a2)

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