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Mat. Zametki, 2020, Volume 108, Issue 4, Pages 561–571 (Mi mz12638)  

On Popular Sums and Differences for Sets with Small Multiplicative Doubling

K. I. Olmezov, A. S. Semchankau, I. D. Shkredov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We improve an estimate for the additive energy of sets $A$ with small product $AA$. The proof uses some properties of level sets of convolutions of the indicator function of $A$, namely, their almost invariance under multiplication by elements of $A$.

Keywords: arithmetic combinatorics, small multiplicative doubling, additive energy, sumset, sum-product theorem.

Funding Agency Grant Number
Russian Science Foundation 19-11-00001
This work was supported by the Russian Science Foundation under grant 19-11-00001.


DOI: https://doi.org/10.4213/mzm12638

Full text: PDF file (528 kB)
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English version:
Mathematical Notes, 2020, 108:4, 557–565

Bibliographic databases:

UDC: 511.178
Received: 18.12.2019
Revised: 08.05.2020

Citation: K. I. Olmezov, A. S. Semchankau, I. D. Shkredov, “On Popular Sums and Differences for Sets with Small Multiplicative Doubling”, Mat. Zametki, 108:4 (2020), 561–571; Math. Notes, 108:4 (2020), 557–565

Citation in format AMSBIB
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