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On multiplicative energy of subsets of varieties

Part of: Designs and configurations Sequences and sets Linear algebraic groups and related topics Harmonic analysis in several variables

Published online by Cambridge University Press:  13 January 2022

Ilya D. Shkredov
Ilya D. Shkredov*
Affiliation:
Department of Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow 119991, Russia
*
e-mail: ilya.shkredov@gmail.com
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Abstract

We obtain a nontrivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to the growth of conjugates classes, estimates of exponential sums, and restriction phenomenon.

Keywords

Multiplicative energyvarietiesrestriction phenomenon

MSC classification

Primary: 11B30: Arithmetic combinatorics; higher degree uniformity
Secondary: 11B75: Other combinatorial number theory 11B99: None of the above, but in this section 05B99: None of the above, but in this section 20G15: Linear algebraic groups over arbitrary fields 42B05: Fourier series and coefficients
Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 1 , February 2023 , pp. 322 - 340
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Copyright
© Canadian Mathematical Society, 2022

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Footnotes

This work is supported by the Russian Science Foundation under grant 19-11-00001.

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