New results on sum-products in R

Abstract

We improve a previous sum--products estimates in R, namely, we obtain that max{|A+A|,|AA|} \gg |A|^{4/3+c}, where c any number less than 5/9813. New lower bounds for sums of sets with small the product set are found. Also we prove some pure energy sum--products results, improving a result of Balog and Wooley, in particular.

18 pages

References in corpus (2)

• Some new inequalities in additive combinatorics
• On sums of Szemerédi--Trotter sets

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• Asymmetric estimates and the sum-product problems
• On product of difference sets for sets of positive density