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Matematicheskie Zametki, 2020, Volume 108, Issue 4, Pages 561–571
DOI: https://doi.org/10.4213/mzm12638 (Mi mzm12638) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (528 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm12638
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.
Received: 18.12.2019
Revised: 08.05.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 4, Pages 557–565
DOI: https://doi.org/10.1134/S000143462009028X
Bibliographic databases:
Document Type: Article
UDC: 511.178
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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