Primitive divisors of sequences associated to elliptic curves with complex multiplication

Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 7(2), 37.

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Abstract
Let P and Q be two points on an elliptic curve defined over a number field K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O, the ideal Bα has a primitive divisor when P is a non-torsion point and there exist two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous results on elliptic divisibility sequences.
Publishing Year
Date Published
2021-05-20
Journal Title
Research in Number Theory
Publisher
Springer Nature
Volume
7
Issue
2
Article Number
37
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Verzobio M. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 2021;7(2). doi:10.1007/s40993-021-00267-9
Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. Springer Nature. https://doi.org/10.1007/s40993-021-00267-9
Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” Research in Number Theory. Springer Nature, 2021. https://doi.org/10.1007/s40993-021-00267-9.
M. Verzobio, “Primitive divisors of sequences associated to elliptic curves with complex multiplication,” Research in Number Theory, vol. 7, no. 2. Springer Nature, 2021.
Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 7(2), 37.
Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” Research in Number Theory, vol. 7, no. 2, 37, Springer Nature, 2021, doi:10.1007/s40993-021-00267-9.
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