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Our first result is a ‘sum–product’ theorem for subsets A of the finite field 𝔽 p , p prime, providing a lower bound on max(| A + A |,| A · A |). As corollary, the second and main result provides new bounds on exponential sums associated to subgroups of the multiplicative group 𝔽 p * .
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Bourgain et al. (2003) studied this question.
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