Bounds on Factors in Z[x]

Abstract

We gather together several bounds on the sizes of coefficients which can appear in factors of polynomials in Z[x]; we include a new bound which was latent in a paper by Mignotte, and a few minor improvements to some existing bounds. We compare these bounds and show that none is universally better than the others. In the second part of the paper we give several concrete examples of factorizations where the factors have "unexpectedly" large coefficients. These examples help us understand why the bounds must be larger than you might expect, and greatly extend the collection published by Collins.

35 pages, no figures

References in corpus (1)

• Factoring polynomials over global fields

Cited by in corpus (4)

• Certifying solutions to overdetermined and singular polynomial systems over Q
• Some conjectures on the maximal height of divisors of $x^n-1$
• Certifying Irreducibility in Z[x]
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