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2019 Some remarks on the asymmetric sum-product phenomenon
Ilya D. Shkredov
Mosc. J. Comb. Number Theory 8(1): 15-41 (2019). DOI: 10.2140/moscow.2019.8.15

Abstract

Using some new observations connected to higher energies, we obtain quantitative lower bounds on max { | A B | , | A + C | } and max { | A B | , | ( A + α ) C | } , where α 0 , in the regime when the sizes of the finite subsets A , B , C of a field differ significantly.

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Ilya D. Shkredov. "Some remarks on the asymmetric sum-product phenomenon." Mosc. J. Comb. Number Theory 8 (1) 15 - 41, 2019. https://doi.org/10.2140/moscow.2019.8.15

Information

Received: 1 December 2017; Published: 2019
First available in Project Euclid: 3 December 2018

zbMATH: 07063260
MathSciNet: MR3864305
Digital Object Identifier: 10.2140/moscow.2019.8.15

Subjects:
Primary: 11B30, 11P70

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.8 • No. 1 • 2019
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