There are Salem numbers with trace $-3$ and every degree at least $34$
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910380447498240 |
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| author | Cherubini, Giacomo Yatsyna, Pavlo |
| author_facet | Cherubini, Giacomo Yatsyna, Pavlo |
| contents | We prove that there exist Salem numbers with trace $-3$ and every even degree $\geq 34$. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace $-3$ and degree $\leq 30$, our result is optimal up to possibly the single value $32$, for which it is expected there are no such numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06536 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | There are Salem numbers with trace $-3$ and every degree at least $34$ Cherubini, Giacomo Yatsyna, Pavlo Number Theory 11R06 (Primary) 11Y40, 11R09, 11C08 (Secondary) We prove that there exist Salem numbers with trace $-3$ and every even degree $\geq 34$. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace $-3$ and degree $\leq 30$, our result is optimal up to possibly the single value $32$, for which it is expected there are no such numbers. |
| title | There are Salem numbers with trace $-3$ and every degree at least $34$ |
| topic | Number Theory 11R06 (Primary) 11Y40, 11R09, 11C08 (Secondary) |
| url | https://arxiv.org/abs/2301.06536 |