| Texto completo | |
| Autor(es): |
Oliveira, Jose Alves
;
Borges, Herivelto
;
Martinez, F. E. Brochero
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | FINITE FIELDS AND THEIR APPLICATIONS; v. 90, p. 25-pg., 2023-05-15. |
| Resumo | |
Let Fqk denote the finite field with qk elements. In this work, we study the number of Fqk-rational points of the affine hypersurfaces given by yq - y = a1xd11 + center dot center dot center dot + asxds s + b. We prove that if b is an element of Fqk has a nonzero trace over Fq, then Weil's bound cannot be achieved and that a sharp bound can be explicitly provided. In the case Trqk/q(b) = 0, we give necessary and sufficient conditions for Weil's bound to be attained. Furthermore, we present several new cases in which formulas for the number of Fqk-rational points can be obtained.(c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 22/15301-5 - Curvas algébricas sobre corpos finitos e aplicações |
| Beneficiário: | Herivelto Martins Borges Filho |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 21/13712-5 - Elementos especiais sobre corpos finitos |
| Beneficiário: | José Alves Oliveira |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |