Humphries, Peter;
(2014)
On the Mertens Conjecture for Function Fields.
International Journal of Number Theory
, 10
(02)
pp. 341-361.
10.1142/S1793042113500978.
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Abstract
We study the natural analogue of the Mertens conjecture in the setting of global function fields. Building on the work of Cha, we show that most hyperelliptic curves do not satisfy the Mertens conjecture, but that if we modify the Mertens conjecture to have a larger constant, then this modified conjecture is satisfied by a positive proportion of hyperelliptic curves.
| Type: | Article |
|---|---|
| Title: | On the Mertens Conjecture for Function Fields |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1142/S1793042113500978 |
| Publisher version: | http://dx.doi.org/10.1142/S1793042113500978 |
| 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: | Mertens Conjecture; Function Field; Möbius Function; Hyperelliptic Curve |
| 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/1569442 |
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