# The Number of Irreducible Factors of a Polynomial, II

Pinner, Christopher and Vaaler, Jeffrey D. (1996) The Number of Irreducible Factors of a Polynomial, II. [Preprint]

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Given a polynomial $f\in k[x]$, $k$ a number field, we consider bounds on the number of cyclotomic factors of $f$ appropriate when the number of non-zero coefficients of the polynomial, $N(f)$, is substantially less than than its degree. In particular we obtain bounds which (apart from a small degree dependence) are only polynomial in $N(f)$. These results arise from variants of Mann's theorem on linear relations between roots of unity.