Bounds For Heights Of Integer Polynomial Factors

: We describe new methods for the estimation of the bounds of the coefficients of proper divisors of integer polynomials in one variable. There exist classes of polynomials for which our estimates are better than those obtained using the polynomial measure or the 2-weighted norm. 1 Introduction A main step in the process of factorization of integer polynomials in one variable is the estimation of the moduli of the coefficients of all possible divisors. Powerful methods are the consideration of estimations using the measure of a polynomial (cf. Mignotte [9]) and the use of weighted norms (cf. Beauzamy [3]). We shall prove that there exist real polynomials for which sharper results may be obtained working directly with the upper bound of the roots instead of the measure. Such are, the polynomials with roots having moduli greater than one, for example Hurwitz polynomials. Alternative results are obtained for the lower bound. We use the following standard notations: IN = the natural numb..