50 citations · 131 across the 25 of their papers we have counts for
5 papers · 1 filter
The uniform primality conjecture for elliptic curves
Graham Everest, Patrick Ingram, Valery Mahe +1
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…
Descent on Elliptic Curves and Hilbert's Tenth Problem
Graham Everest, Kirsten Eisentraeger
Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's T…
Dirichlet series for finite combinatorial rank dynamics
G. Everest, R. Miles, S. Stevens +1
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit c…
Primitive divisors on twists of the Fermat cubic
Graham Everest, Patrick Ingram, Shaun Stevens
We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u^3+v^3=m, with m cube-free, all the terms beyond the first have a primitive divisor.
On primitive divisors of n^2+b
Graham Everest, Glyn Harman
We study primitive divisors of terms of the sequence P_n=n^2+b, for a fixed integer b which is not a negative square. It seems likely that the number of terms with a primitive divi…