Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T19:37:10.245Z Has data issue: false hasContentIssue false
  • English
  • Français

Integral points on elliptic curves over function fields

Part of: Arithmetic algebraic geometry Curves

Published online by Cambridge University Press:  09 April 2009

W. -C. Chi ,
K. F. Lai  and
K. -S. Tan
W. -C. Chi
Affiliation:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan e-mail: wchi@math.ntnu.edu.tw
K. F. Lai
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia e-mail: kflai@math.usyd.edu.au
K. -S. Tan
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan e-mail: tan@math.ntu.edu.tw
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove a new formula for the number of integral points on an elliptic curve over a function field without assuming that the coefficient field is algebraically closed. This is an improvement on the standard results of Hindry-Silverman.

MSC classification

Secondary: 11G05: Elliptic curves over global fields 14H52: Elliptic curves
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 2 , October 2004 , pp. 197 - 208
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Evertse, J.-H., ‘On equations in S-units and the Thue-Mahler equation’, Invent. Math. 75 (1984), 561–584.CrossRefGoogle Scholar
[2]Evertse, J.-H., ‘On equations in two S-units over function fields of characteristic 0’, Acta Arith. 47 (1986), 233–253.CrossRefGoogle Scholar
[3]Hindry, M. and Silverman, J. H., ‘The canonical height and integral points on elliptic curves’, Invent. Math. 93 (1988), 419–450.CrossRefGoogle Scholar
[4]Lang, S., Elliptic curves: Diophantine analysis (Springer, Berlin, 1978).CrossRefGoogle Scholar
[5]Mason, R. C., Diophantine equations over function fields, London Math. Soc. Lecture Note Ser. 96 (Cambridge University Press, Cambridge, 1984).CrossRefGoogle Scholar
[6]Silverman, J. H., ‘A quantitative version of Siegel's theorem’, J. Reine Angew. Math. 378 (1987), 60–100.Google Scholar
[7]Tan, K.-S., ‘A 2-division formula for elliptic curves’, preprint, (National Taiwan University, Taipei, 2002).Google Scholar