The uniform primality conjecture for elliptic curves

Details The uniform primality conjecture for elliptic curves The uniform primality conjecture for elliptic curves

2007-12-17

arxiv.org/abs/0712.2696v1

Mathematics

Number Theory

24 pages, 1 figure

Scientific paper

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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