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Title: | Autour d'un théorème de Stein |
Authors: | Najib, Salah |
Keywords: | Polinomio irreducible;Polinomio compuesto;Espectro de un polinomio;Stein's desigual;Irreducible polynomial;Composite polynomial;Spectrum of a polynomial;Stein's inequality |
Issue Date: | 2008 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | Let 𝐾 be a field of characteristic zero, k ̅ an algebraic closure of K and P (X, Y) a non constant polynomial, with coefficients in K. For ¸ λ𝜖 k ̅, denote the number of distinct irreducible factors f⋋,i in a factorization of P– λ ¸ over (k ) ̅by ո(λ). We rewrite without the jacobian derivation aspect of Stein's proof (1989) for showing the following statement : if P is non-composite then ∑ ⋋(n(λ) – 1) is at most equal to deg(P) –1. |
URI: | http://hdl.handle.net/10662/14891 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 23, nº 2 (2008) |
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0213-8743_23_2_173.pdf | 161,78 kB | Adobe PDF | View/Open |
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