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  • There is some work by Igor Shparlinski on an exponential version of sum-product in finite fields, where one looks at the sets {g^a+g^b: a in A, b in B} and {g^{ab}: a in A, b in B} for some generator g, and also on elliptic curve versions in which one looks at { x(aP) + x(bP): a in A, b in B} and {x(abP): a in A, b in B}, where P is a point on an elliptic curve of some order p, A and B are sets in
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