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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 $$F$$.

##### MSC:
 11C08 Polynomials in number theory 12D05 Polynomials in real and complex fields: factorization