p-cycles, S2-sets and Curves with Many Points

  • Álvaro Garzón


We construct S 2 -sets contained in the integer interval I q − 1 := [1, q − 1] with q = p^n,p a prime number and n ∈ Z +, by using the p-adic expansion of integers. Such sets comefrom considering p-cycles of length n. We give some criteria in particular cases whichallow us to glue them to obtain good S 2 -sets. After that we construct algebraic curvesover the finite field F q with many rational points via minimal (F p , F p )-polynomials whose exponent is an S 2 -set.

Como citar
GARZÓN, Álvaro. p-cycles, S2-sets and Curves with Many Points. Revista de Ciencias, [S.l.], v. 21, n. 1, p. 55-78, abr. 2018. ISSN 2248-4000. Disponible en: <http://nexus.univalle.edu.co/index.php/revista_de_ciencias/article/view/6340>. Fecha de acceso: 24 jun. 2018 doi: https://doi.org/10.25100/rc.v21i1.6340.
Artículos de Investigación - Matemática