Value sets of Dickson polynomials over finite fields

AbstractLet Fq denote the finite field of order q where q is a prime power. If a ∈ Fq and d ≥ 1 is an integer, define the Dickson polynomial gd(x, a) = ∑t=0[d2] (d(d−t))(td−t)(−atxd−2t. Let {gd(x, a) | x ∈ Fq} denote the image or value set of the polynomial gd(x, a). In this paper we determine the cardinality of the value set for the Dickson polynomial gd(x, a) over the finite field Fq