Nombres de Pisot, nombres de Salem et la conjecture de Lehmer
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912606007066624 |
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| author | Amara, Mohamed |
| author_facet | Amara, Mohamed |
| contents | We investigate the relationship between the set S of Pisot numbers and the set T of Salem numbers. Salem first established that: " every Pisot number is an accumulation point of the set T ". Building on Boyd's method, we show that every accumulation point of T belongs to S. Together, these results imply that the union S U T forms a closed subset of the real half-line ]1,+infinity[. Consequently, this settles Boyd's conjecture while disproving Lehmer's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nombres de Pisot, nombres de Salem et la conjecture de Lehmer Amara, Mohamed Number Theory We investigate the relationship between the set S of Pisot numbers and the set T of Salem numbers. Salem first established that: " every Pisot number is an accumulation point of the set T ". Building on Boyd's method, we show that every accumulation point of T belongs to S. Together, these results imply that the union S U T forms a closed subset of the real half-line ]1,+infinity[. Consequently, this settles Boyd's conjecture while disproving Lehmer's conjecture. |
| title | Nombres de Pisot, nombres de Salem et la conjecture de Lehmer |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.21402 |