Strong inverse conjecture for the Gowers norm
Let ppp be prime, k≥1k\geq1k≥1, G=FpnG=\mathbb{F}_p^nG=Fpn, and D={z∈C:∣z∣≤1}\mathbb D=\{z\in\mathbb C:|z|\leq1\}D={z∈C:∣z∣≤1}. Let ε:N→R+\varepsilon:\mathbb N\to\mathbb R^+ε:N→R+ be decreasing, and let Polyk(G)\mathrm{Poly}^k(G)Polyk(G) be…