Primitive divisors of sequences associated to elliptic curves

Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 209(4), 378–390.

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Abstract
Let be a sequence of points on an elliptic curve defined over a number field K. In this paper, we study the denominators of the x-coordinates of this sequence. We prove that, if Q is a torsion point of prime order, then for n large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two points P and Q on the elliptic curve, we prove a lower bound for the number of primes p such that P is in the orbit of Q modulo p.
Publishing Year
Date Published
2020-04-01
Journal Title
Journal of Number Theory
Publisher
Elsevier
Volume
209
Issue
4
Page
378-390
ISSN
IST-REx-ID

Cite this

Verzobio M. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 2020;209(4):378-390. doi:10.1016/j.jnt.2019.09.003
Verzobio, M. (2020). Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2019.09.003
Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” Journal of Number Theory. Elsevier, 2020. https://doi.org/10.1016/j.jnt.2019.09.003.
M. Verzobio, “Primitive divisors of sequences associated to elliptic curves,” Journal of Number Theory, vol. 209, no. 4. Elsevier, pp. 378–390, 2020.
Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 209(4), 378–390.
Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” Journal of Number Theory, vol. 209, no. 4, Elsevier, 2020, pp. 378–90, doi:10.1016/j.jnt.2019.09.003.
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