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| |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.
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