| Full text | |
| Author(s): |
Oliveira, Jose Alves
;
Borges, Herivelto
;
Martinez, F. E. Brochero
Total Authors: 3
|
| Document type: | Journal article |
| Source: | FINITE FIELDS AND THEIR APPLICATIONS; v. 90, p. 25-pg., 2023-05-15. |
| Abstract | |
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) | |
| FAPESP's process: | 22/15301-5 - Algebraic curves over finite fields and applications |
| Grantee: | Herivelto Martins Borges Filho |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/13712-5 - Special Elements over finite fields |
| Grantee: | José Alves Oliveira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |