Some new results on the higher energies I
Number Theory
2023-04-11 v2 Combinatorics
Abstract
We obtain a generalization of the recent Kelley--Meka result on sets avoiding arithmetic progressions of length three. In our proof we develop the theory of the higher energies. Also, we discuss the case of longer arithmetic progressions, as well as a general family of norms, which includes the higher energies norms and Gowers norms.
Keywords
Cite
@article{arxiv.2303.16348,
title = {Some new results on the higher energies I},
author = {Ilya D. Shkredov},
journal= {arXiv preprint arXiv:2303.16348},
year = {2023}
}
Comments
26 pages, the second part of the appendix is added