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http://repositorio.ufla.br/jspui/handle/1/58847| Title: | On the number of rational points on artin-schreier hypersurfaces |
| Keywords: | Weil's bound Artin-Schreier equations Finite fields Gauss sums |
| Issue Date: | Sep-2023 |
| Publisher: | Elsevier |
| Citation: | OLIVEIRA, J. A.; BORGES, H.; MARTÍNEZ, F. E. B. On the number of rational points on artin-schreier hypersurfaces. Finite Fields and Their Applications, [S.l.], v. 90, Sept. 2023. |
| Abstract: | Let denote the finite field with elements. In this work, we study the number of -rational points of the affine hypersurfaces given by . We prove that if has a nonzero trace over , then Weil's bound cannot be achieved and that a sharp bound can be explicitly provided. In the case , 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 -rational points can be obtained. |
| URI: | https://www.sciencedirect.com/science/article/pii/S1071579723000710 http://repositorio.ufla.br/jspui/handle/1/58847 |
| Appears in Collections: | DMM - Artigos publicados em periódicos |
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