An inverse theorem for the Gowers $U^{s+1}[N]$-norm
An inverse theorem for the Gowers $U^{s+1}[N]$-norm
This is an announcement of the proof of the inverse conjecture for the Gowers $U^{s+1}[N]$-norm for all $s \geq 3$; this is new for $s \geq 4$, the cases $s = 1,2,3$ having been previously established. More precisely we outline a proof that if $f : [N] \rightarrow [-1,1]$ is …