Criteria of maximality and minimality of van der Geer-van der Vlugt curves
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915070843289600 |
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| author | Ito, Tetsushi Tatematsu, Ren Tsushima, Takahiro |
| author_facet | Ito, Tetsushi Tatematsu, Ren Tsushima, Takahiro |
| contents | The van der Geer-van der Vlugt curves are Artin-Schreier coverings of the affine line defined by linearized polynomials over finite fields. We give several criteria for them to be maximal or minimal, i.e. attaining the upper or lower bound in the Hasse-Weil inequalities. We also study the $L$-polynomials of certain generalizations of van der Geer-van der Vlugt curves. As applications, we find several maximal (or minimal) curves among them. Our proof is based on an explicit formula of $L$-polynomials recently obtained by Takeuchi and the third author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Criteria of maximality and minimality of van der Geer-van der Vlugt curves Ito, Tetsushi Tatematsu, Ren Tsushima, Takahiro Number Theory Primary: 14F20, 14G15, Secondary: 11M38, 11G20 The van der Geer-van der Vlugt curves are Artin-Schreier coverings of the affine line defined by linearized polynomials over finite fields. We give several criteria for them to be maximal or minimal, i.e. attaining the upper or lower bound in the Hasse-Weil inequalities. We also study the $L$-polynomials of certain generalizations of van der Geer-van der Vlugt curves. As applications, we find several maximal (or minimal) curves among them. Our proof is based on an explicit formula of $L$-polynomials recently obtained by Takeuchi and the third author. |
| title | Criteria of maximality and minimality of van der Geer-van der Vlugt curves |
| topic | Number Theory Primary: 14F20, 14G15, Secondary: 11M38, 11G20 |
| url | https://arxiv.org/abs/2412.00902 |