학술논문

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm
Document Type
Working Paper
Source
Subject
Mathematics - Combinatorics
Mathematics - Dynamical Systems
Mathematics - Number Theory
Language
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.
Comment: 100 pages