Polynomial Factorization: Sharp Bounds, Efficient Algorithms

A new coefficient bound is established for factoring univariate polynomials over the integers. Unlike an overall bound, the new bound limits the size of the coefficients of at least one irreducible factor of the given polynomial. The single-factor bound is derived from the weighted norm introduced in Beauzamyet al. (1990) and is almost optimal. Effective use of this bound in p-adic lifting results in a more efficient factorization algorithm. A full example and comparisons with known coefficient bounds are included.