Abstract
Let χ be a non-trivial character of F × q , and let g(x) be its associated Gauss sum. It is well known that g(χ) = e(χ)√q, where |e(χ)| = 1. Using the p-adic gamma function, we give a new proof of a result of Evans which gives necessary and sufficient conditions for e(χ) to be a root of unity.
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