First and Second Moment Analysis of Dickson Polynomials of the Second Kind - Zhijian Wang (Journal of Mathematics)
For a given positive integer k and a polynomial fx over the finite field Fq, the k-th moment of fx is defined by ∑x∈Fqfkx. In this paper, we explicitly present formulas related to the first and second moments of Dickson polynomials of the second kind Enx,a. From these formulas, one can evaluate the sum ∑x∈FqEnx,a and ∑x∈FqEn2x,a for the given finite field Fq and the parameter a with arbitrary n.