On the distances between Pisot numbers generating the same number field
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913228901056512 |
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| author | Zaimi, Toufik |
| author_facet | Zaimi, Toufik |
| contents | A well-known result, due to Meyer, states that the set P of Pisot numbers, generating a real algebraic number field K, is uniformly discrete and relatively dense in the set of positive real number. In the present paper, we show that P is contained is the set, say D, of the differences of elements of P, and the complement of P in D is not finite. Also, we prove that if K is totally real, then the elements of D are the algebraic integers of K whose images under the action of all embeddings of K into R, other than the identity of K, belong to the interval (-2,2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distances between Pisot numbers generating the same number field Zaimi, Toufik Number Theory 11R06, 11R04, 12D10 A well-known result, due to Meyer, states that the set P of Pisot numbers, generating a real algebraic number field K, is uniformly discrete and relatively dense in the set of positive real number. In the present paper, we show that P is contained is the set, say D, of the differences of elements of P, and the complement of P in D is not finite. Also, we prove that if K is totally real, then the elements of D are the algebraic integers of K whose images under the action of all embeddings of K into R, other than the identity of K, belong to the interval (-2,2). |
| title | On the distances between Pisot numbers generating the same number field |
| topic | Number Theory 11R06, 11R04, 12D10 |
| url | https://arxiv.org/abs/2402.06182 |