Open Accessp-cycles, S2-sets and Curves with Many Points
Author(s) -
Álvaro Garzón
Publication year - 2018
Publication title -
revista de ciencias (on line)/revista de ciencias
Language(s) - English
Resource type - Journals
eISSN - 2248-4000
pISSN - 0121-1935
DOI - 10.25100/rc.v21i1.6340
Subject(s) - mathematics , integer (computer science) , combinatorics , prime (order theory) , interval (graph theory) , exponent , set (abstract data type) , algebraic number , discrete mathematics , mathematical analysis , computer science , linguistics , programming language , philosophy
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 nite eld F q with many rational points via minimal (F p , F p )-polynomials whose exponent is an S 2 -set.