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First and Second Moment Analysis of Dickson Polynomials of the Second Kind

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  • Zhijian Wang

Abstract

For a given positive integer k and a polynomial f(x) over the finite field Fq, the k‐th moment of f(x) 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 En(x, 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.

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Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5569145
DOI: 10.1155/jom/5569145
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