The uniform primality conjecture for elliptic curves

Everest, Graham, Ingram, Patrick, Mahé, Valéry and Stevens, Shaun (2008) The uniform primality conjecture for elliptic curves. Acta Arithmetica, 134 (2). pp. 157-181. ISSN 0065-1036

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Abstract

An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over the rational function field, unconditionally. In the latter case, a uniform bound is obtained on the index of a prime term. Sharpened versions of these techniques are shown to lead to explicit results where all the irreducible terms can be computed.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://arxiv.org/abs/0712.2696
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:44
Last Modified:	13 May 2025 23:49
URI:	https://ueaeprints.uea.ac.uk/id/eprint/20952
DOI:	10.4064/aa134-2-7

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