Gowers norms of multiplicative functions in progressions on average

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2 Scopus citations


Let μ be the Möbius function and let k ≥ 1. We prove that the Gowers Uk-norm of μ restricted to progressions {n ≤ X : n ≡ aq (mod q)} is o(1) on average over q ≤ X1/2-σ for any σ > 0, where aq (mod q) is an arbitrary residue class with (aq, q) = 1. This generalizes the Bombieri-Vinogradov inequality for μ, which corresponds to the special case k = 1.

Original languageEnglish
Pages (from-to)961-982
Number of pages22
JournalAlgebra and Number Theory
Issue number4
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Mathematical Sciences Publishers.


  • Bombieri-Vinogradov theorem
  • Gowers norms
  • Multiplicative functions

ASJC Scopus subject areas

  • Algebra and Number Theory


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