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A height inequality for rational points on elliptic curves implied by the abc-conjecture

Title data

Kühn, Ulf ; Müller, Jan Steffen:
A height inequality for rational points on elliptic curves implied by the abc-conjecture.
In: Functiones et Approximatio Commentarii Mathematici. Vol. 52 (2015) Issue 1 . - pp. 127-132.
ISSN 0208-6573
DOI: https://doi.org/10.7169/facm/2015.52.1.10

Abstract in another language

n this short note we show that the uniform abc-conjecture puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we use a variant of Vojta’s height inequality formulated by Mochizuki. As an application, we generalize a result of Silverman on elliptic non-Wieferich primes.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: 2010 Mathematics Subject Classification: primary: 11G05; secondary: 11G50
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 May 2017 11:02
Last Modified: 04 May 2017 11:02
URI: https://eref.uni-bayreuth.de/id/eprint/36945