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

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.