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Dec 6, 2017 at 12:45 comment added Padraig Ó Catháin The full power of the Weil bound is not required - character theory and Gauss sums suffice. Notes of Babai give an explicit bound of q < 85 for this problem: people.cs.uchicago.edu/~laci/reu02/fourier.pdf
Nov 9, 2017 at 4:25 history answered Felipe Voloch CC BY-SA 3.0