Equidistribution of Primitive Normal Elements in Finite Fields
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910016809730048 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | Let $q=p^k$ be a prime power, let $n\geq2$ be an integer and let $\mathbb{F}_{q^n}$ be a finite field. It is shown that the set of primitive normal elements is a Salem set. Furthermore, it is proved that this set is strongly equidistributed in the finite field. Similar results are proved for the set of quadratic residues and the set of primitive roots modulo a large prime $p\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equidistribution of Primitive Normal Elements in Finite Fields Carella, N. A. General Mathematics Primary 11T30, 12E20, Secondary 11T06, 11N37 Let $q=p^k$ be a prime power, let $n\geq2$ be an integer and let $\mathbb{F}_{q^n}$ be a finite field. It is shown that the set of primitive normal elements is a Salem set. Furthermore, it is proved that this set is strongly equidistributed in the finite field. Similar results are proved for the set of quadratic residues and the set of primitive roots modulo a large prime $p\geq 3$. |
| title | Equidistribution of Primitive Normal Elements in Finite Fields |
| topic | General Mathematics Primary 11T30, 12E20, Secondary 11T06, 11N37 |
| url | https://arxiv.org/abs/2602.09048 |