On primitive points of elliptic curves with complex multiplication

Chen, Yen Mei J.; Yu, Jing

doi:10.1016/j.jnt.2005.02.005

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Cited by 3 publications

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“…We now attempt to give a brief account of more recent results. In 2005, Chen and Yu in [5] extended the positive density results of [10] to include the possibility that the complex multiplication is given by a non-maximal order. In 2010, Akbary, Ghioca and V.K.…”

Section: Introductionmentioning

confidence: 99%

Primitive submodules for Drinfeld modules

Kuo

Tweedle

2015

Math. Proc. Camb. Phil. Soc.

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The ring A = $\mathbb{F}$r[T] and its fraction field k, where r is a power of a prime p, are considered as analogues of the integers and rational numbers respectively. Let K/k be a finite extension and let φ be a Drinfeld A-module over K of rank d and Γ ⊂ K be a finitely generated free A-submodule of K, the A-module structure coming from the action of φ. We consider the problem of determining the number of primes ℘ of K for which the reduction of Γ modulo ℘ is equal to $\mathbb{F}$℘ (the residue field of the prime ℘). We can show that there is a natural density of primes ℘ for which Γ mod ℘ is equal to $\mathbb{F}$℘. In certain cases, this density can be seen to be positive.

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Section: Introductionmentioning

confidence: 99%