eprintid: 1569442 rev_number: 19 eprint_status: archive userid: 608 dir: disk0/01/56/94/42 datestamp: 2017-10-25 14:44:02 lastmod: 2020-08-02 00:03:25 status_changed: 2017-10-25 14:44:02 type: article metadata_visibility: show creators_name: Humphries, Peter title: On the Mertens Conjecture for Function Fields ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 keywords: Mertens Conjecture; Function Field; Möbius Function; Hyperelliptic Curve note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2014-03 date_type: published official_url: http://dx.doi.org/10.1142/S1793042113500978 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1410911 doi: 10.1142/S1793042113500978 lyricists_name: Humphries, Peter lyricists_id: PHUMP20 actors_name: Humphries, Peter actors_id: PHUMP20 actors_role: owner full_text_status: public publication: International Journal of Number Theory volume: 10 number: 02 pagerange: 341-361 issn: 1793-7310 citation: Humphries, Peter; (2014) On the Mertens Conjecture for Function Fields. International Journal of Number Theory , 10 (02) pp. 341-361. 10.1142/S1793042113500978 <https://doi.org/10.1142/S1793042113500978>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1569442/1/Humphries_on_the_mertens_conjecture_for_function.pdf