Granville, A;
Harper, AJ;
Soundararajan, K;
(2018)
A more intuitive proof of a sharp version of Halász's theorem.
Proceedings of the American Mathematical Society
, 146
(10)
pp. 4099-4104.
10.1090/proc/14095.
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Abstract
We prove a sharp version of Halász's theorem on sums ∑_{n≤χ} ƒ(n) of multiplicative functions ƒ with |ƒ(n)| ≤ 1. Our proof avoids the "average of averages" and "integration over α" manoeuvres that are present in many of the existing arguments. Instead, motivated by the circle method, we express ∑_{n≤χ} ƒ(n) as a triple Dirichlet convolution and apply Perron's formula.
| Type: | Article |
|---|---|
| Title: | A more intuitive proof of a sharp version of Halász's theorem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/proc/14095 |
| Publisher version: | https://doi.org/10.1090/proc/14095 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10083303 |
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