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- W4256688424 abstract "Let $F(x)$ be a polynomial with coefficients in an algebraic number field $k$. We estimate the number of irreducible cyclotomic factors of $F$ in $k[x]$, the number of irreducible noncyclotomic factors of $F$, the number of $n$th roots of unity among the roots of $F$, and the number of primitive $n$th roots of unity among the roots of $F$. All of these quantities are counted with multiplicity and estimated by expressions which depend explicitly on $k$, on the degree of $F$ and height of $F$, and (when appropriate) on $n$. We show by constructing examples that some of our results are essentially sharp." @default.
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- W4256688424 date "1993-10-01" @default.
- W4256688424 modified "2023-09-26" @default.
- W4256688424 title "The Number of Irreducible Factors of a Polynomial. I" @default.
- W4256688424 doi "https://doi.org/10.2307/2154300" @default.
- W4256688424 hasPublicationYear "1993" @default.
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