Vol. 295, No. 1, 2018

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Effective results on linear dependence for elliptic curves

Min Sha and Igor E. Shparlinski

Vol. 295 (2018), No. 1, 123–144
Abstract

Given a subgroup Γ of rational points on an elliptic curve E defined over of rank r 1 and any sufficiently large x 2, assuming that the rank of Γ is less than r, we give upper and lower bounds on the canonical height of a rational point Q which is not in the group Γ but belongs to the reduction of Γ modulo every prime p x of good reduction for E.

Keywords
elliptic curve, linear dependence, pseudolinearly dependent point, pseudomultiple, canonical height
Mathematical Subject Classification 2010
Primary: 11G05, 11G50
Milestones
Received: 10 June 2016
Revised: 18 October 2017
Accepted: 29 January 2018
Published: 13 March 2018
Authors
Min Sha
School of Mathematics and Statistics
University of New South Wales
Sydney, NSW
Australia
Igor E. Shparlinski
School of Mathematics and Statistics
University of New South Wales
Sydney, NSW
Australia