The number of rational points of a class of superelliptic curves

Autor(es)

Oliveira, Jose Alves ; Oliveira, Daniela ; Martinez, F. E. Brochero

• Tipo de documento: Artigo Científico
• Fonte: FINITE FIELDS AND THEIR APPLICATIONS; v. 91, p. 24-pg., 2023-10-01.

Resumo

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)

• Processo FAPESP: 21/13712-5 - Elementos especiais sobre corpos finitos
• Beneficiário: José Alves Oliveira
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado