On Salem numbers which are exceptional units II
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909102543732736 |
|---|---|
| author | Zaimi, Toufik |
| author_facet | Zaimi, Toufik |
| contents | We show that for any natural number $n$ satisfying $n\equiv 4 \mod 8$ and $n\not\equiv 0 \mod 5$, and for any odd integer $t\geq \frac{n+6}{2}$ there are infinitely many Salem numbers $α$ of degree $2t$ such that $α^n-1$ is a unit. This result, obtained using a generalization of a construction due to Gross and McMullen [5], partially completes the main result of [7]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Salem numbers which are exceptional units II Zaimi, Toufik Number Theory 11R06, 11R04, 11Y40 We show that for any natural number $n$ satisfying $n\equiv 4 \mod 8$ and $n\not\equiv 0 \mod 5$, and for any odd integer $t\geq \frac{n+6}{2}$ there are infinitely many Salem numbers $α$ of degree $2t$ such that $α^n-1$ is a unit. This result, obtained using a generalization of a construction due to Gross and McMullen [5], partially completes the main result of [7]. |
| title | On Salem numbers which are exceptional units II |
| topic | Number Theory 11R06, 11R04, 11Y40 |
| url | https://arxiv.org/abs/2402.07481 |