eprintid: 1569443 rev_number: 17 eprint_status: archive userid: 608 dir: disk0/01/56/94/43 datestamp: 2017-10-25 14:57:45 lastmod: 2020-08-02 00:03:26 status_changed: 2017-10-25 14:57:45 type: article metadata_visibility: show creators_name: HUMPHRIES, PETER title: On the Mertens Conjecture for Elliptic Curves Over Finite Fields ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: We introduce an analogue of the Mertens conjecture for elliptic curves over finite fields. Using a result of Waterhouse, we classify the isogeny classes of elliptic curves for which this conjecture holds in terms of the size of the finite field and the trace of the Frobenius endomorphism acting on the curve. date: 2014-02 date_type: published official_url: http://dx.doi.org/10.1017/S0004972712001116 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1410912 doi: 10.1017/S0004972712001116 lyricists_name: Humphries, Peter lyricists_id: PHUMP20 actors_name: Humphries, Peter actors_id: PHUMP20 actors_role: owner full_text_status: public publication: Bulletin of the Australian Mathematical Society volume: 89 number: 01 pagerange: 19-32 issn: 1755-1633 citation: HUMPHRIES, PETER; (2014) On the Mertens Conjecture for Elliptic Curves Over Finite Fields. Bulletin of the Australian Mathematical Society , 89 (01) pp. 19-32. 10.1017/S0004972712001116 <https://doi.org/10.1017/S0004972712001116>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1569443/1/Humphries_on_the_mertens_conjecture_for_elliptic_curves.pdf