On sum sets of sets having small product set

By Sergei V. Konyagin, Ilya D. Shkredov. 2015

67 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/783e6c835fe4ca2a9885b617424e952279e0543d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. M. Rudnev
2. Ilya D. Shkredov
3. Oliver Roche-Newton
4. Sophie Stevens

In Discrete Mathematics and Combinatorics

1. Ilya D. Shkredov
2. M. Rudnev
3. Oliver Roche-Newton
4. Sophie Stevens
5. Frank de Zeeuw
6. Brendan Murphy
7. Tom Sanders
8. Ben Joseph Green

In Geometry and Topology

1. M. Rudnev
2. Oliver Roche-Newton
3. Ilya D. Shkredov
4. Tom Sanders
5. Ben Joseph Green

Citations in the corpus

• New sum-product type estimates over finite fields (2014, background): “amp; |A|4/3, in the notation of Remark 8. This is weaker than (15) and much weaker than the optimal consequence in this vein of (13), (14), holding for real and complex numbers. See also Theorem 9 in [18]. NEW SUM-PRODUCT TYPE ESTIMATES OVER FINITE FIELDS 9 Theorem 14. Let A,B,C ⊆ F. Suppose that |B”