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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-N32
F5507-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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Received: 25.10.2018
Revised: 04.02.2019
Accepted:10.02.2019
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