On the fourth-order linear recurrence formula related to classical Gauss sums

Abstract

Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.

Keywords

• the classical gauss sums
• fourth-order linear recurrence formula
• analytic method
• character sums
• 11l05
• 11l07
• 11t24