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A more intuitive proof of a sharp version of Halász's theorem
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Granville, Andrew, Harper, Adam and Soundararajan, Kannan (2018) A more intuitive proof of a sharp version of Halász's theorem. Proceedings of the American Mathematical Society, 146 . 4099-4104 . doi:10.1090/proc/14095 ISSN 0002-9939.
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Official URL: https://doi.org/10.1090/proc/14095
Abstract
We prove a sharp version of Halász's theorem on sums $ \sum _{n \leq x} f(n)$ of multiplicative functions $ f$ with $ \vert f(n)\vert\le 1$. Our proof avoids the ``average of averages'' and ``integration over $ \alpha $'' manoeuvres that are present in many of the existing arguments. Instead, motivated by the circle method, we express $ \sum _{n \leq x} f(n)$ as a triple Dirichlet convolution and apply Perron's formula.
Item Type: | Journal Article | |||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Functions, Number theory | |||||||||||||||||||||
Journal or Publication Title: | Proceedings of the American Mathematical Society | |||||||||||||||||||||
Publisher: | American Mathematical Society | |||||||||||||||||||||
ISSN: | 0002-9939 | |||||||||||||||||||||
Official Date: | 15 May 2018 | |||||||||||||||||||||
Dates: |
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Volume: | 146 | |||||||||||||||||||||
Page Range: | 4099-4104 | |||||||||||||||||||||
DOI: | 10.1090/proc/14095 | |||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
Copyright Holders: | American Mathematical Society | |||||||||||||||||||||
Date of first compliant deposit: | 9 February 2018 | |||||||||||||||||||||
Date of first compliant Open Access: | 28 September 2018 | |||||||||||||||||||||
RIOXX Funder/Project Grant: |
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