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Gauss sums over finite fields and roots of unity.

Lemke Oliver, Robert J.

2011.

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Let χ be a non-trivial character of F×q, and let g(χ) be its associated Gauss sum. It is well known that g(χ) = ε(χ) √q, where |ε(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 ε(χ) to be a root of unity. (c) 2010 American Mathematical Society

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Oliver, Robert J. Lemke. "Gauss Sums over Finite Fields and Roots of Unity." Proceedings of the American Mathematical Society 139, no. 04 (April 1, 2011): 1273-1273. doi:10.1090/s0002-9939-2010-10662-7.