Abstract

AbstractLet q = pr with p an odd prime, and Fq denote the finite field of q elements. Let Tr : Fq → Fp be the usual trace map and set ζp = exp(2πi/p). For any positive integer e, define the (modified) Gauss sum gr(e) byRecently, Evans gave an elegant determination of g1(12) in terms of g1(3), g1(4) and g1(6) which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum gr(12).

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