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On sum sets of sets having small product set

  • S. V. Konyagin
  • I. D. Shkredov
Article

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 AR with |AA| ≤ |A|4/3.

Keywords

Real Number STEKLOV Institute Discrete Math Schwarz Inequality Absolute Constant 
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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

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

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