Inter relationship between numbers congruent and elliptic curves
Curves with many rational points over finite fields and their applications in cod...
Rational points and automorphisms on algebraic curves over finite fields
| Full text | |
| Author(s): |
Oliveira, Jose Alves
;
Oliveira, Daniela
;
Martinez, F. E. Brochero
Total Authors: 3
|
| Document type: | Journal article |
| Source: | FINITE FIELDS AND THEIR APPLICATIONS; v. 91, p. 24-pg., 2023-10-01. |
| Abstract | |
In this paper, we study the number of Fqn-rational points on the affine curve Xd,a,b given by the equationyd = axTr(x) + b,where Tr denote the trace function from Fqn to Fq and d is a positive integer. In particular, we present bounds for the number of Fq-rational points on Xd,a,b and, for the cases where d satisfies a natural condition, explicit formulas for the number of rational points are obtained. Particularly, a complete characterization is given for the case d = 2. As a consequence of our results, we compute the number of elements & alpha; in Fqn such that & alpha; and Tr(& alpha;) are quadratic residues in Fqn.& COPY; 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 21/13712-5 - Special Elements over finite fields |
| Grantee: | José Alves Oliveira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |