Some new infinite families of monogenic polynomials with non-squarefree discriminant

DOI10.4064/aa200211-21-7zbMath1465.11204OpenAlexW3093152582MaRDI QIDQ5854710

Leonard Jones

Publication date: 17 March 2021

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa200211-21-7

zbMATH Keywords

discriminantirreducibletrinomialmonogenic

Mathematics Subject Classification ID

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

Related Items (11)

On necessary and sufficient conditions for the monogeneity of a certain class of polynomials ⋮ On common index divisors and monogenity of certain number fields defined by x⁵ + ax² + b ⋮ Infinite families of monogenic quadrinomials, quintinomials and sextinomials ⋮ On non monogenity of certain number fields defined by trinomials \(x^6 + ax^3 + b\) ⋮ On common index divisor and monogenity of certain number fields defined by trinomials X⁶ + AX + B ⋮ On index and monogenity of certain number fields defined by trinomials ⋮ Unnamed Item ⋮ Infinite families of non-monogenic trinomials ⋮ Some new polynomial discriminant formulas ⋮ Discriminants of special quadrinomials ⋮ Monogenic trinomials with non-squarefree discriminant

Cites Work

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• Factorization of polynomials over finite fields
• A construction of polynomials with squarefree discriminants
• Advanced Topics in Computional Number Theory
• Monogenic polynomials with non-squarefree discriminant
• A BRIEF NOTE ON SOME INFINITE FAMILIES OF MONOGENIC POLYNOMIALS
• On the discriminant of certain quadrinomials
• The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments

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