Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm

James Leng, Ashwin Sah, Mehtaab Sawhney

Type: Preprint

Publication Date: 2024-02-27

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2402.17994

Abstract

We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution of nilsequences. In a companion paper, this result will be used to improve the bounds on Szemer\'{e}di's theorem.

Locations

arXiv (Cornell University) - View - PDF

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