Primitive divisors of sequences associated to elliptic curves
Number Theory
2023-11-15 v1
Abstract
Let be a sequence of points on an elliptic curve defined over a number field . In this paper, we study the denominators of the -coordinates of this sequence. We prove that, if is a torsion point of prime order, then for large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and the Lang-Trotter conjecture.
Cite
@article{arxiv.1906.00632,
title = {Primitive divisors of sequences associated to elliptic curves},
author = {Matteo Verzobio},
journal= {arXiv preprint arXiv:1906.00632},
year = {2023}
}