Schinzel's bound on the number of irreducible factors of Kf

Let ff be the polynomial considered in the source, let KfKf denote its associated polynomial vocabulary description, let Ω1(f)\Omega_1(f) be the number of irreducible factors of KfKf over Q\mathbb{Q}, counted with multiplicities, and let f2\lVert f\rVert_2 be the norm used in the source. Schinzel's conjecture. There exists a function ψ\psi such that

Ω1(f)ψ(f2).\Omega_1(f)\leq\psi(\lVert f\rVert_2).

The conjecture proposes a bound on the number of irreducible factors in terms of the size of ff; the supplied context does not establish whether this bound has been proved or disproved.

Sources & referencesView supporting material

Primary source

Jacques Carette and James H. Davenport, “The Power of Vocabulary: The Case of Cyclotomic Polynomials”, arXiv:1002.0012 (2010).

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