On Popular Sums and Differences for Sets with Small Multiplicative Doubling

We improve an estimate for the additive energy of sets with small product . The proof uses some properties of level sets of convolutions of the indicator function of , namely, their almost invariance under multiplication by elements of .

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Bibliographische Detailangaben
Veröffentlicht in:	Mathematical Notes 2020-10, Vol.108 (3-4), p.557-565
Hauptverfasser:	Ol’mezov, K. I., Semchenkov, A. S., Shkredov, I. D.
Format:	Artikel
Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Mathematics Mathematics and Statistics Multiplication
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We improve an estimate for the additive energy of sets with small product . The proof uses some properties of level sets of convolutions of the indicator function of , namely, their almost invariance under multiplication by elements of .
ISSN:	0001-4346 1067-9073 1573-8876
DOI:	10.1134/S000143462009028X