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Torsion points with multiplicatively dependent coordinates on elliptic curves

2020; Wiley; Volume: 52; Issue: 5 Linguagem: Inglês

10.1112/blms.12363

1469-2120

Fabrizio Barroero, Min Sha,

Cryptography and Residue Arithmetic

Bulletin of the London Mathematical SocietyVolume 52, Issue 5 p. 807-815 Research Article Torsion points with multiplicatively dependent coordinates on elliptic curves Fabrizio Barroero, fbarroero@gmail.com Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Murialdo 1, Roma, 00146 ItalySearch for more papers by this authorMin Sha, Corresponding Author shamin2010@gmail.com Department of Computing, Macquarie University, Balaclava Road, Sydney, NSW, 2109 Australia shamin2010@gmail.comSearch for more papers by this author Fabrizio Barroero, fbarroero@gmail.com Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Murialdo 1, Roma, 00146 ItalySearch for more papers by this authorMin Sha, Corresponding Author shamin2010@gmail.com Department of Computing, Macquarie University, Balaclava Road, Sydney, NSW, 2109 Australia shamin2010@gmail.comSearch for more papers by this author First published: 15 June 2020 https://doi.org/10.1112/blms.12363 The first author had done part of this work under the support of the Swiss National Science Foundation [165525]. The second author was supported by a Macquarie University Research Fellowship. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication. Volume52, Issue5October 2020Pages 807-815 RelatedInformation