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