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Abstract
Using some new observations connected to higher energies, we obtain quantitative lower
bounds on
max { | A B | , | A
+
C | }
and
max { | A B | , | ( A
+
α ) C | } , where
α ≠ 0 , in the regime when the
sizes of the finite subsets
A , B , C
of a field differ significantly.
Keywords
sum-product, expanders, exponential sums
Mathematical Subject Classification 2010
Primary: 11B30, 11P70
Milestones
Received: 1 December 2017
Published: 11 August 2018