The Number of Irreducible Factors of a Polynomial. I

DOI10.2307/2154300zbMath0787.11045OpenAlexW4256688424MaRDI QIDQ3142099

Jeffrey D. Vaaler, Christopher G. Pinner

Publication date: 15 May 1994

Full work available at URL: https://doi.org/10.2307/2154300

zbMATH Keywords

heightdegreepolynomialexplicit estimates\(n\)-th cyclotomic polynomialnumber of \(n\)-th roots of unitynumber of irreducible cyclotomic factorsnumber of irreducible noncyclotomic factorsnumber of primitive roots of unity

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Diophantine inequalities (11J25) Polynomials (irreducibility, etc.) (11R09)

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Cites Work

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• On the number of irreducible factors of a polynomial II
• On a theorem of Dobrowolski about the product of conjugate numbers
• On a conjecture of D. H. Lehmer
• Resultants of Cyclotomic Polynomials
• The distribution of values of the Euler function
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer