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New results on sums and products in ℝ

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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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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    S. V. Konyagin & I. D. Shkredov

Authors
  1. S. V. Konyagin
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  2. I. D. Shkredov
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Correspondence to S. V. Konyagin.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 294, pp. 87–98.

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Konyagin, S.V., Shkredov, I.D. New results on sums and products in ℝ. Proc. Steklov Inst. Math. 294, 78–88 (2016). https://doi.org/10.1134/S0081543816060055

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  • DOI: https://doi.org/10.1134/S0081543816060055

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