On the Zeta function and the automorphism group of the generalized Suzuki curve
| Autor: | Mariana Coutinho, Herivelto Borges |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Automorphism group
Applied Mathematics General Mathematics 010102 general mathematics Prime number 01 natural sciences 11G20 14G05 14G10 14H37 law.invention Riemann zeta function Combinatorics Mathematics - Algebraic Geometry symbols.namesake Invertible matrix law FOS: Mathematics symbols 0101 mathematics CURVAS ALGÉBRICAS Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | For p p an odd prime number, q 0 = p t q_{0}=p^{t} , and q = p 2 t − 1 q=p^{2t-1} , let X G S \mathcal {X}_{\mathcal {G}_{\mathcal {S}}} be the nonsingular model of Y q − Y = X q 0 ( X q − X ) . \begin{equation*} Y^{q}-Y=X^{q_{0}}(X^{q}-X). \end{equation*} In the present work, the number of F q n \mathbb {F}_{q^{n}} -rational points and the full automorphism group of X G S \mathcal {X}_{\mathcal {G}_{\mathcal {S}}} are determined. In addition, the L-polynomial of this curve is provided, and the number of F q n \mathbb {F}_{q^{n}} -rational points on the Jacobian J X G S J_{\mathcal {X}_{\mathcal {G}_{\mathcal {S}}}} is used to construct étale covers of X G S \mathcal {X}_{\mathcal {G}_{\mathcal {S}}} , some with many rational points. |
| Databáze: | OpenAIRE |
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