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.
@article{MZM_2020_108_4_a7,
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/}
}
TY - JOUR AU - K. I. Olmezov AU - A. S. Semchankau AU - I. D. Shkredov TI - On Popular Sums and Differences for Sets with Small Multiplicative Doubling JO - Matematičeskie zametki PY - 2020 SP - 561 EP - 571 VL - 108 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2020_108_4_a7/ LA - ru ID - MZM_2020_108_4_a7 ER -
%0 Journal Article %A K. I. Olmezov %A A. S. Semchankau %A I. D. Shkredov %T On Popular Sums and Differences for Sets with Small Multiplicative Doubling %J Matematičeskie zametki %D 2020 %P 561-571 %V 108 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2020_108_4_a7/ %G ru %F MZM_2020_108_4_a7
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/