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arXiv · 0712.2696

The uniform primality conjecture for elliptic curves

Graham Everest·Patrick Ingram·Valery Mahe·Shaun Stevens
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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.

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Graham Everest, Patrick Ingram, Valery Mahe, Shaun Stevens. 2007-12-17. The uniform primality conjecture for elliptic curves. https://doi.org/10.4064/aa134-2-7

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