Vol. 10, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Linear relations in families of powers of elliptic curves

Fabrizio Barroero and Laura Capuano

Vol. 10 (2016), No. 1, 195–214
Abstract

Motivated by recent work of Masser and Zannier on simultaneous torsion on the Legendre elliptic curve Eλ of equation Y 2 = X(X 1)(X λ), we prove that, given n linearly independent points P1(λ),,Pn(λ) on Eλ with coordinates in (λ) ¯, there are at most finitely many complex numbers λ0 such that the points P1(λ0),,Pn(λ0) satisfy two independent relations on Eλ0. This is a special case of conjectures about unlikely intersections on families of abelian varieties.

Keywords
linear relations, elliptic curves, unlikely intersections
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 11G50, 11U09, 14K05
Milestones
Received: 29 January 2015
Revised: 1 October 2015
Accepted: 27 November 2015
Published: 14 February 2016
Authors
Fabrizio Barroero
Classe di Scienze
Scuola Normale Superiore
Piazza dei Cavalieri 7
I-56126 Pisa
Italy
Laura Capuano
Classe di Scienze
Scuola Normale Superiore
Piazza dei Cavalieri 7
I-56126 Pisa
Italy