The uniform primality conjecture for elliptic curves

Graham Everest, Patrick Ingram, Valéry Mahé, Shaun Stevens

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6 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)157-181
Number of pages25
JournalActa Arithmetica
Volume134
Issue number2
DOIs
Publication statusPublished - 2008

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