English

Primitive divisors of sequences associated to elliptic curves

Number Theory 2023-11-15 v1

Abstract

Let {nP+Q}n0\{nP+Q\}_{n\geq0} be a sequence of points on an elliptic curve defined over a number field KK. In this paper, we study the denominators of the xx-coordinates of this sequence. We prove that, if QQ is a torsion point of prime order, then for nn 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.

Keywords

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}
}