Integer sequences from elliptic curves
Number Theory
2023-11-07 v2 Algebraic Geometry
Abstract
We indicate that given an integer coordinate point on an elliptic curve y^2+axy+by=x^3+cx^2+dx+e we can identify an integer sequence whose Hankel transform is a Somos-4 sequence, and whose Hankel determinants can be used to determine the coordinates of the multiples of this point. In reverse, given the coordinates of the multiples of an integer point on such an elliptic curve, we conjecture the form of a continued fraction generating function that expands to give a sequence with the above properties.
Cite
@article{arxiv.2306.05025,
title = {Integer sequences from elliptic curves},
author = {Paul Barry},
journal= {arXiv preprint arXiv:2306.05025},
year = {2023}
}
Comments
14 pages. Typos corrected