English

The uniform primality conjecture for elliptic curves

Number Theory 2015-05-13 v1

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.

Keywords

Cite

@article{arxiv.0712.2696,
  title  = {The uniform primality conjecture for elliptic curves},
  author = {Graham Everest and Patrick Ingram and Valery Mahe and Shaun Stevens},
  journal= {arXiv preprint arXiv:0712.2696},
  year   = {2015}
}

Comments

24 pages, 1 figure

R2 v1 2026-06-21T09:54:47.997Z