Quasipolynomial bounds on the inverse theorem for the Gowers Us+1[N]-norm
Abstract
We prove quasipolynomial bounds on the inverse theorem for the Gowers Us+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\'edi's theorem.
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