Geodesic
New results on sums and products in~$\mathbb R$
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 87-98.

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

We improve previous sum-product estimates in $\mathbb R$; namely, we prove the inequality $\max\{|A+A|,|AA|\}\gg|A|^{4/3+c}$, where $c$ is any number less than $5/9813$. New lower bounds for sums of sets with small product set are found. We also obtain results on the additive and multiplicative energies; in particular, we improve a result of Balog and Wooley. 
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S. V. Konyagin; I. D. Shkredov. New results on sums and products in~$\mathbb R$. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 87-98. http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a4/

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