Let be the Möbius function and let . We prove that the Gowers -norm of restricted to progressions is on average over for any , where is an arbitrary residue class with . This generalizes the Bombieri–Vinogradov inequality for , which corresponds to the special case .
"Gowers norms of multiplicative functions in progressions on average." Algebra Number Theory 11 (4) 961 - 982, 2017. https://doi.org/10.2140/ant.2017.11.961