Infinite families of reciprocal monogenic polynomials and their Galois groups

zbMath1487.11096MaRDI QIDQ2075861

Leonard Jones

Publication date: 16 February 2022

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://nyjm.albany.edu/j/2021/27-57.html

zbMATH Keywords

Galois groupirreducibilityreciprocal polynomialmonogenity

Mathematics Subject Classification ID

Algebraic field extensions (12F05) Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (2)

RECIPROCAL MONOGENIC QUINTINOMIALS OF DEGREE ⋮ GALOIS GROUPS OF RECIPROCAL SEXTIC POLYNOMIALS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Square-free values of \(f(p)\), \(f\) cubic
• On a relationship between Chebyshev polynomials and Toeplitz determinants
• Elementary criteria for irreducibility of \(f(X^r)\)
• A new condition equivalent to the Ankeny-Artin-Chowla conjecture
• Monogenic cyclotomic compositions
• Sextic reciprocal monogenic dihedral polynomials
• Symmetric polynomials in the symplectic alphabet and the change of variables \(z_j = x_j + x_j^{-1}\)
• Factoring Quartic Polynomials: A Lost Art
• An Elementary Test for the Galois Group of a Quartic Polynomial
• The transitive groups of degree up to eleven⁺
• Fibonacci and Lucas Numbers With Applications
• Galois Groups of Even Sextic Polynomials
• The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments
• The irreducibility of power compositional sextic polynomials and their Galois groups
• On the Jacobians of Curves Defined by the Generalized Laguerre Polynomials
• The Factorization of the Cyclotomic Polynomials mod p

This page was built for publication: Infinite families of reciprocal monogenic polynomials and their Galois groups