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math.NT2017★ 22 cited
Some remarks on the asymmetric sum--product phenomenon
Ilya D. Shkredov
Using some new observations connected to higher energies, we obtain quantitative lower bounds on and , in the regime when…
math.NT2017
Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields
Simon Macourt, Ilya D. Shkredov, Igor E. Shparlinski
We give a new bound on colinear triples in subgroups of prime finite fields and use it to give some new bounds on exponential sums with trinomials.