A class of irreducible polynomials

• Autorzy: Joshua Harrington , Lenny Jones
• Języki publikacji: EN

Abstrakty

EN

Let
$f(x) = xⁿ + k_{n-1}x^{n-1} + k_{n-2}x^{n-2} + ⋯ +k₁x + k₀ ∈ ℤ[x]$,
where
$3 ≤ k_{n-1} ≤ k_{n-2} ≤ ⋯ ≤ k₁ ≤ k₀ ≤ 2k_{n-1} - 3$.
We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2k_{n-1} - 3$ on the coefficients of f(x) is the best possible in this situation.

Kategorie tematyczne

• 11C08: Polynomials
• 11R09: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 113-119

Daty

wydano

2013

Twórcy

autor

Joshua Harrington

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

autor

Lenny Jones

• Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, U.S.A.

Identyfikatory

DOI

10.4064/cm132-1-9