Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Invariant of Chen-Kuan for Abelian Varieties

  • Moon, Hyunsuk (Department of Mathematics, Kyungpook National University)
  • Received : 2016.03.22
  • Accepted : 2016.07.05
  • Published : 2016.09.23
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Abstract

Let A be an abelian variety over a global field K. We show that, in "many" cases, Chen-Kuan's invariant M(A[n]), that is the average number of n-torsion points of A over various residue fields of K, has the minimal possible value.

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References

  1. Yen-Mei J. Chen and Yen-Liang Kuan, On the distribution of torsion points modulo primes, Bull. Aust. Math. Soc., 86(2012), 339-347. https://doi.org/10.1017/S0004972712000019
  2. P. M. Cohn, Algebra, Second edition Volume 3, John Wiley & Sons, 1991.
  3. Hsiu-Lien Huang, The average number of torsion points on elliptic curves, J. Number Theory, 135(2014), 374-389. https://doi.org/10.1016/j.jnt.2013.08.004
  4. H. Moon, On the invariant M($A_{/K}$; n) of Chen-Kuan for Galois representations, Proc. Japan Acad., 90(2014), 98-100. https://doi.org/10.3792/pjaa.90.98
  5. J.-P. Serre, Resume des cours de 1985-1986, Annuaire du College de France (1986), 95-99.

Cited by

  1. On the Calculation of the Number of Galois Orbits vol.56, pp.4, 2016, https://doi.org/10.5666/KMJ.2016.56.4.1135