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

• Autores: Álvaro Garzón R.
• Localización: Revista de Ciencias Universidad del Valle, ISSN-e 2248-4000, ISSN 0121-1935, Vol. 21, Nº. 1, 2017, 78 págs.
• Idioma: español
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• Resumen

  • 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.