Abstract

Let F q be a finite field with q= p f elements, where p is a prime number and f is a positive integer. For a nonprincipal multiplicative character χ and a nontrivial additive character ψ on F q , it is well known that Gauss sum g(χ,ψ)=∑ t∈ F q ∗ χ(t)ψ(t) has absolute value q . In this paper, we investigate when g(χ,ψ)/ q is a root of unity.

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