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2017 Gowers norms of multiplicative functions in progressions on average
Xuancheng Shao
Algebra Number Theory 11(4): 961-982 (2017). DOI: 10.2140/ant.2017.11.961

Abstract

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(modq)} is o(1) on average over q X12σ for any σ > 0, where aq(modq) 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.

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Xuancheng Shao. "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

Information

Received: 15 July 2016; Revised: 2 December 2016; Accepted: 29 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06735376
MathSciNet: MR3665642
Digital Object Identifier: 10.2140/ant.2017.11.961

Subjects:
Primary: 11P32
Secondary: 11B30, 11N13

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2017
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