Corpus ID: 119313761

New results on sum-products in R

@article{Konyagin2016NewRO,
  title={New results on sum-products in R},
  author={Sergei Konyagin and Ilya D. Shkredov},
  journal={arXiv: Combinatorics},
  year={2016}
}
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. 
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