On characterization of prime divisors of the index of a quadrinomial
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916554622369792 |
|---|---|
| author | Chatterjee, Tapas Kumar, Karishan |
| author_facet | Chatterjee, Tapas Kumar, Karishan |
| contents | Let $θ$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $θ$ over the rationals. Let $K=\mathbb{Q}(θ)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $f(x).$ As a fascinating corollary, we deduce necessary and sufficient conditions for the monogenity of the field $K=\mathbb{Q}(θ),$ where $θ$ is associated with certain quadrinomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On characterization of prime divisors of the index of a quadrinomial Chatterjee, Tapas Kumar, Karishan Number Theory Primary: 11R04, 11R29, 11Y40, Secondary: 11R09, 11R21 Let $θ$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $θ$ over the rationals. Let $K=\mathbb{Q}(θ)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $f(x).$ As a fascinating corollary, we deduce necessary and sufficient conditions for the monogenity of the field $K=\mathbb{Q}(θ),$ where $θ$ is associated with certain quadrinomials. |
| title | On characterization of prime divisors of the index of a quadrinomial |
| topic | Number Theory Primary: 11R04, 11R29, 11Y40, Secondary: 11R09, 11R21 |
| url | https://arxiv.org/abs/2408.14524 |