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Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm
Published 28 Feb 2024 in math.CO, math.DS, and math.NT | (2402.17994v3)
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.
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