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

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {K. I. Olmezov and A. S. Semchankau and I. D. Shkredov},
     title = {On {Popular} {Sums} and {Differences} for {Sets} with {Small} {Multiplicative} {Doubling}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {561--571},
     publisher = {mathdoc},
     volume = {108},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_4_a7/}
}
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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/