Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve
Abstract
Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $\phi:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $\phi(P)=(Q_1,\dots, Q_m)$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2023
- DOI:
- arXiv:
- arXiv:2309.09699
- Bibcode:
- 2023arXiv230909699B
- Keywords:
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- Mathematics - Number Theory;
- 11B39;
- 11G05;
- 11G10;
- 14K02