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arXiv:2402.17994 [math.CO]AbstractReferencesReviewsResources

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

James Leng, Ashwin Sah, Mehtaab Sawhney

Published 2024-02-28, updated 2024-04-10Version 2

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.

Comments: 100 pages
Categories: math.CO, math.DS, math.NT
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