Journal of Number Theory
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 J. Number Theory, 2019, Volume 201, Pages 124–134 (Mi jnt6)

If $A+A$ is small then $AAA$ is superquadratic

Oliver Roche-Newtona, Ilya D. Shkredovbcd

a Johann Radon Institute for Computational and Applied Mathematics(RICAM), 69 Altenberger Straße, Linz, Austria
b Steklov Mathematical Institute, ul. Gubkina, 8, 119991 Moscow, Russia
c IITP RAS, Bolshoy Karetny per. 19, 127994 Moscow, Russia
d MIPT, Institutskii per. 9, 141701 Dolgoprudnii, Russia

 Funding Agency Grant Number Austrian Science Fund P 30405-N32F5507-N26 Oliver Roche-Newton was partially supported by the Austrian Science Fund FWF Project P 30405-N32 as well as by the Austrian Science Fund (FWF), Project F5507-N26, which is a part of the Special Research Program Quasi-Monte Carlo Methods: Theory and Applications. We are grateful to George Shakan, Audie Warren and Dinitry Zhelezov for various helpful conversations and advice. We also thank the anonymous referee for helpful comments and corrections.

DOI: https://doi.org/10.1016/j.jnt.2019.02.026

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Revised: 04.02.2019
Accepted:10.02.2019
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