The number of irreducible factors of a polynomial. I
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- by Christopher G. Pinner and Jeffrey D. Vaaler PDF
- Trans. Amer. Math. Soc. 339 (1993), 809-834 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 339 (1993), 809-834
- MSC: Primary 11R09; Secondary 12E05
- DOI: https://doi.org/10.1090/S0002-9947-1993-1150018-X
- MathSciNet review: 1150018