Geodesic
Calculation of a Gauss sum via the discrete Fourier transform
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 90-95

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The explicit formula for a Gauss sum is proved using the discrete Fourier transform. The Gauss quadratic reciprocity law is established as a corollary. 
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     title = {Calculation of a {Gauss} sum via the discrete {Fourier} transform},
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A. V. Ustinov. Calculation of a Gauss sum via the discrete Fourier transform. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 90-95. http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a7/