Glesser, Philippe; Mignotte, Maurice An inequality about irreducible factors of integer polynomials. II. (English) Zbl 0739.11010 Applied algebra, algebraic algorithms and error-correcting codes, Proc. 8th Int. Conf., AAECC-8, Tokyo/Jap. 1990, Lect. Notes Comput. Sci. 508, 260-266 (1991). [For the entire collection see Zbl 0727.00017; for part I, cf. J. Number Theory 30, 156-166 (1988: Zbl 0648.12002).]Let \(F(x)\) be a polynomial with integral coefficients. The height of \(F\), written \(H(F)\), is defined as the maximum of the moduli of the coefficients of \(F\). The authors prove the following useful upper bound for the height of an irreducible factor \(P(x)\) of \(F(x)\), \[ H(P)\leq(e/2)^{\sqrt d}(d+2\sqrt{d}+1)^{1/2+\sqrt d}M(F)^{1+\sqrt d}, \] where \(d=\deg(P)\) and \(M(F)\) denotes the Mahler measure of \(F\). Reviewer: K.S.Williams (Ottawa) Cited in 1 Document MSC: 11C08 Polynomials in number theory 12D05 Polynomials in real and complex fields: factorization Keywords:integer polynomial; upper bound; height; irreducible factor; Mahler measure Citations:Zbl 0727.00017; Zbl 0648.12002 PDF BibTeX XML Cite \textit{P. Glesser} and \textit{M. Mignotte}, Lect. Notes Comput. Sci. None, 260--266 (1991; Zbl 0739.11010)