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
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 22 Oct 2019 09:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/20952
DOI: 10.4064/aa134-2-7

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