Granville, A;
Harper, AJ;
Soundararajan, K;
(2015)
Mean values of multiplicative functions over function fields.
Research in Number Theory
, 1
(25)
10.1007/s40993-015-0023-5.
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Abstract
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation.
| Type: | Article |
|---|---|
| Title: | Mean values of multiplicative functions over function fields |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40993-015-0023-5 |
| Publisher version: | http://dx.doi.org/ 10.1007/s40993-015-0023-5 |
| 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. |
| Keywords: | Multiplicative functions Halász’s theorem Function fields |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/1522171 |
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