Granville, A;
Koukoulopoulos, D;
(2019)
Beyond the LSD method for the partial sums of multiplicative functions.
Ramanujan Journal
10.1007/s11139-018-0119-3.
(In press).
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Abstract
The Landau–Selberg–Delange method gives an asymptotic formula for the partial sums of a multiplicative function f whose prime values are α on average. In the literature, the average is usually taken to be α with a very strong error term, leading to an asymptotic formula for the partial sums with a very strong error term. In practice, the average at the prime values may only be known with a fairly weak error term, and so we explore here how good an estimate this will imply for the partial sums of f, developing new techniques to do so.
| Type: | Article |
|---|---|
| Title: | Beyond the LSD method for the partial sums of multiplicative functions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11139-018-0119-3 |
| Publisher version: | https://doi.org/10.1007/s11139-018-0119-3 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Averages of multiplicative functions, Landau–Selberg–Delange method, Wirsing’s theorem |
| 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/10073250 |
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