Monogenic trinomials and class numbers of related quadratic fields

2024/12/29 by Jones, Lenny
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.20443

Abstract

We say that a monic polynomial f(x)∈ \mathbb Z[x] of degree N≥ 2 is monogenic if f(x) is irreducible over \mathbb Q and \1,θ,θ²,… ,θ^N-1\ is a basis for the ring of integers of \mathbb Q(θ), where f(θ)=0. In this article, we investigate the divisibility of the class numbers of quadratic fields \mathbb Q(√δ) for certain families of monogenic trinomials f(x)=x^N+Ax+B, where δ≠ ± 1 is a squarefree divisor of the discriminant of f(x).

Related

• Monogenic Cyclic Quartic Trinomials
• The monogenicity and Galois groups of certain reciprocal quintinomials
• Monogenic cyclic trinomials of the form x⁴+cx+d
• The Irreducibility and Monogenicity of Power-Compositional Trinomials
• On characterization of Monogenic number fields associated with certain quadrinomials and its applications