Geodesic
On Popular Sums and Differences for Sets with Small Multiplicative Doubling
Matematičeskie zametki, Tome 108 (2020) no. 4, pp. 561-571.

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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. 
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K. I. Olmezov; A. S. Semchankau; I. D. Shkredov. On Popular Sums and Differences for Sets with Small Multiplicative Doubling. Matematičeskie zametki, Tome 108 (2020) no. 4, pp. 561-571. http://geodesic.mathdoc.fr/item/MZM_2020_108_4_a7/

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