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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
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm12638https://doi.org/10.4213/mzm12638 https://www.mathnet.ru/eng/mzm/v108/i4/p561
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