Gowers norms of multiplicative functions in progressions on average

Abstract

Let µ be the Möbius function and let k ≥ 1.We prove that the Gowers U knorm of µ restricted to progressions {n ≤ X : n ≡ a q (mod q)} is o(1) on average over q ≤ X 1/2-σ for any σ > 0, where a q (mod q) is an arbitrary residue class with (a q , q) = 1.This generalizes the Bombieri-Vinogradov inequality for µ, which corresponds to the special case k = 1.

Locations

• Algebra & Number Theory - View
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
• DataCite API - View