Additive energies of subsets of discrete cubes

Xuancheng Shao

doi:10.1017/prm.2024.126

Additive energies of subsets of discrete cubes

Xuancheng Shao

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a positive integer, define tn to be the smallest number such that the additive energy E(A) of any subset and any d is at most. Trivially, we have and by considering. In this note, we investigate the behaviour of tn for large n and obtain the following non-trivial bounds: where c > 0 is an absolute constant.

Original language	English
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
DOIs	https://doi.org/10.1017/prm.2024.126
State	Accepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

ASJC Scopus subject areas

General Mathematics

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10.1017/prm.2024.126

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Additive energies of subsets of discrete cubes

Abstract

Bibliographical note

ASJC Scopus subject areas

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