Elementary bounds on character sums with polynomial arguments
نویسنده
چکیده
Again, for small degrees d, this is the kind of cancellation that we would expect from a sum of q random points on the unit circle. Looking at the whole argument in totality, what we just did is highly highly dependent on P (X) being a single monomial. The multiplicativity of the monomial brings the characters of the multiplicative group into play. For a general polynomial P (X), we have no such option. We now give a different argument for bounding |S|. This argument will be amenable to generalization to all polynomials.
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