Abstract
We improve the sum–product result of Solymosi in R; namely, we prove that max{|A + A|, |AA|} ****** |A|4/3+c, where c > 0 is an absolute constant. New lower bounds for sums of sets with small product set are found. Previous results are improved effectively for sets A ⊂ R with |AA| ≤ |A|4/3.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Vol. 290, pp. 304–316.
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Konyagin, S.V., Shkredov, I.D. On sum sets of sets having small product set. Proc. Steklov Inst. Math. 290, 288–299 (2015). https://doi.org/10.1134/S0081543815060255
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DOI: https://doi.org/10.1134/S0081543815060255