The average number of torsion points on elliptic curves

Huang, Hsiu-Lien

doi:10.1016/j.jnt.2013.08.004

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“…It is known that the limit M (ρ n ) exists and it is equal to the number of orbits of [3]). In general, M (ρ n ) ≥ n + 1 since each π i V n is stable under the Galois action and so U n,i for each 0 ≤ i ≤ n − 1 is stable.…”

Section: Introductionmentioning

confidence: 99%

On the Invariant of Chen-Kuan for Abelian Varieties

Moon¹

2016

Kyungpook mathematical journal

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Section: Introductionmentioning

confidence: 99%

On the Invariant of Chen-Kuan for Abelian Varieties

Moon¹

2016

Kyungpook mathematical journal

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On the moments of torsion points modulo primes and their applications

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Wong

2020

Int. J. Number Theory

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Let [Formula: see text] be the group of [Formula: see text]-torsion points of a commutative algebraic group [Formula: see text] defined over a number field [Formula: see text]. For a prime [Formula: see text] of [Formula: see text], we let [Formula: see text] be the number of [Formula: see text]-solutions of the system of polynomial equations defining [Formula: see text] when reduced modulo [Formula: see text]. Here, [Formula: see text] is the residue field at [Formula: see text]. Let [Formula: see text] denote the number of primes [Formula: see text] of [Formula: see text] such that [Formula: see text]. We then, for algebraic groups of dimension one, compute the [Formula: see text]th moment limit [Formula: see text] by appealing to the Chebotarev density theorem. We further interpret this limit as the number of orbits of the action of the absolute Galois group of [Formula: see text] on [Formula: see text] copies of [Formula: see text] by an application of Burnside’s Lemma. These concrete examples suggest a possible approach for determining the number of orbits of a group acting on [Formula: see text] copies of a set.

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On the Calculation of the Number of Galois Orbits

Moon¹

2016

Kyungpook mathematical journal

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The average number of torsion points on elliptic curves

Cited by 3 publications

References 4 publications

On the Invariant of Chen-Kuan for Abelian Varieties

On the Invariant of Chen-Kuan for Abelian Varieties

On the moments of torsion points modulo primes and their applications

On the Calculation of the Number of Galois Orbits

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