Sextic reciprocal monogenic dihedral polynomials

DOI10.1007/s11139-020-00310-wzbMath1487.11095OpenAlexW3046095858MaRDI QIDQ2054721

Leonard Jones

Publication date: 3 December 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-020-00310-w

zbMATH Keywords

Galois groupdihedral groupirreducible polynomialmonogenic polynomialsymmetric polynomialpalindromic polynomialreciprocal polynomialChebyshev polynomial of the first kindself-reciprocal polynomialdiscriminant of a polynomial

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Algebraic field extensions (12F05) Other number fields (11R21) Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (2)

GALOIS GROUPS OF RECIPROCAL SEXTIC POLYNOMIALS ⋮ Infinite families of reciprocal monogenic polynomials and their Galois groups

Uses Software

• Magma
• Maple
• SageMath

Cites Work

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• \(\text{PSL}(2,5)\) sextic fields with a power basis
• Symmetric polynomials in the symplectic alphabet and the change of variables \(z_j = x_j + x_j^{-1}\)
• The transitive groups of degree up to eleven⁺
• Advanced Topics in Computional Number Theory
• 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
• The Factorization of the Cyclotomic Polynomials mod p

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