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- W4221157015 abstract "Let $K = mathbb{Q} (th) $ be a number field generated by a complex root $th$ of a monic irreducible trinomial of type $ F(x)= x^{2^r}+ax^m+b in Z[x]$ and $Z_K$ its ring of integers. In this paper, we study the monogenity of $K$. More precisely, when $m=1$, we provide some explicit conditions on $a$, $b$, and $r$ for which $K$ is not monogenic. We also construct a family of irreducible trinomials which are not monogenic, but their roots generate monogenic number fields. To illustrate our results, we give some computational examples." @default.
- W4221157015 created "2022-04-03" @default.
- W4221157015 creator A5077155727 @default.
- W4221157015 date "2022-03-19" @default.
- W4221157015 modified "2023-09-26" @default.
- W4221157015 title "On monogenity of certain number fields defined by $x^{2^r}+ax^m+b$" @default.
- W4221157015 doi "https://doi.org/10.48550/arxiv.2203.10413" @default.
- W4221157015 hasPublicationYear "2022" @default.
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