Our first result is a ‘sum-product’ theorem for subsets A of the finite field Fp, p prime, providing a lower bound on max (|A + A|, |A · A|). The second and main result provides new bounds on exponential sums ∑ x 1 , … , x k ∈ A exp ( 2 π i x 1 … x k ξ / p ) where A⊂Fp.
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Bourgain et al. (2006) studied this question.