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On the Mertens Conjecture for Function Fields

Humphries, Peter; (2014) On the Mertens Conjecture for Function Fields. International Journal of Number Theory , 10 (02) pp. 341-361. 10.1142/S1793042113500978. Green open access

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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.ucl.ac.uk/id/eprint/1569442
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