Abstract
We improve previous sum–product estimates in ℝ; namely, we prove the inequality max{|A + A|, |AA|} ≫ |A|4/3+c, where c is any number less than 5/9813. New lower bounds for sums of sets with small product set are found. We also obtain results on the additive and multiplicative energies; in particular, we improve a result of Balog and Wooley.
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Schedule a callMore From: Proceedings of the Steklov Institute of Mathematics
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