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arXiv · 2309.09699

Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

Stefan Barańczuk·Bartosz Naskręcki·Matteo Verzobio
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Abstract

Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $ϕ:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $ϕ(P)=(Q_1,\dots, Q_m)$ with $\text{Rank}_\mathbb{Z}(\langle Q_1,\dots, Q_m\rangle)=1$. We will study a divisibility sequence related to the point $P$ and show its relation with elliptic divisibility sequences.

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Stefan Barańczuk, Bartosz Naskręcki, Matteo Verzobio. 2025-07-24. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. https://doi.org/10.1016/j.jnt.2025.06.001

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