New results on sums and products in ℝ

  • S. V. Konyagin
  • I. D. Shkredov


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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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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