On index divisors and monogenity of certain number fields defined by trinomials

2022/03/24 by Lhoussain El Fadil, Fadil, Lhoussain El
Mathematics · #11Y40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #D.2 #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.13353

openalex publication_date 2022/03/24 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let K be a number field generated by a root þ of a monic irreducible trinomial F(x) = xⁿ+ax^m+b ∈ \Z[x]. In this paper, we study the problem of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic. As applications, we show that there are infinite families of non-monogenic number fields defined by trinomials of degree n=2^r⋅3^k with r and k two positive integers. We also give infinite families of non-monogenic sextic number fields defined by trinomials. Some illustrating examples are giving at the end of this paper.

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