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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Height uniformity for integral points on elliptic curves
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by Su-ion Ih PDF
Trans. Amer. Math. Soc. 358 (2006), 1657-1675 Request permission

Abstract:

We recall the result of D. Abramovich and its generalization by P. Pacelli on the uniformity for stably integral points on elliptic curves. It says that the Lang-Vojta conjecture on the distribution of integral points on a variety of logarithmic general type implies the uniformity for the numbers of stably integral points on elliptic curves. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.
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Additional Information
  • Su-ion Ih
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602–7403
  • Address at time of publication: Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309-0395
  • MR Author ID: 703039
  • Email: ih@math.uga.edu
  • Received by editor(s): March 6, 2004
  • Received by editor(s) in revised form: June 9, 2004
  • Published electronically: August 1, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 1657-1675
  • MSC (2000): Primary 11G35, 11G50, 14G05
  • DOI: https://doi.org/10.1090/S0002-9947-05-03760-8
  • MathSciNet review: 2186991