1 citations · 1 across the 5 of their papers we have counts for
7 papers
The perfect power problem for elliptic curves over function fields
Gunther Cornelissen, Jonathan Reynolds
We generalise the Siegel-Voloch theorem about S-integral points on elliptic curves as follows: let K/F denote a global function field over a finite field F of characteristic p>3, l…
Matrix divisibility sequences
Gunther Cornelissen, Jonathan Reynolds
We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated t…
Perfect powers generated by the twisted Fermat cubic
Jonathan Reynolds
On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. It is shown that there are finite…
Perfect powers in elliptic divisibility sequences
Jonathan Reynolds
It is shown that there are finitely many perfect powers in an elliptic divisibility sequence whose first term is divisible by 2 or 3. For Mordell curves the same conclusion is show…
On the pre-image of a point under an isogeny and Siegel's theorem
Jonathan Reynolds
Consider a rational point on an elliptic curve under an isogeny. Suppose that the action of Galois partitions the set of its pre-images into n orbits. It is shown that all such poi…
On the pre-image of a point under an isogeny
Jonathan Reynolds
Given a rational point on a curve in a rational isogeny class, a natural question concerns the field of definition of its pre-images. The multiplication by m endomorphism is a powe…