Kyungpook Mathematical Journal

  • 제56권4호
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  • Pages.1135-1140
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  • 2016
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On the Calculation of the Number of Galois Orbits

  • Moon, Hyunsuk (Department of Mathematics, Kyungpook National University)
  • 투고 : 2016.08.15
  • 심사 : 2016.09.22
  • 발행 : 2016.12.23
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초록

Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.

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참고문헌

  1. K. Arai, On uniform lower bound of the Galois image associated to elliptic curves, J. Theor. Nombres Bordeaux, 20(2008), 23-43. https://doi.org/10.5802/jtnb.614
  2. A. Cadoret and A. Tamagawa, A uniform open image theorem for $\ell$-adic representations II, Duke Math. J. 162(2013), 2301-2344. https://doi.org/10.1215/00127094-2323013
  3. Y. J. Chen and Y. Kuan, On the distribution of torsion points modulo primes, Bull. Aust. Math. Soc. 86(2012), 339-347. https://doi.org/10.1017/S0004972712000019
  4. H. 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
  5. B. Mazur, Rational points on modular curves, Modular functions of one variable V, Lecture Notes in Math., Vol. 601, Springer, Berlin (1977), 107-148.
  6. H. Moon, On the invariant $M(A_{/K},\;n)$ of Chen-Kuan for Galois representations, Proc. Japan Acad. 90(2014), 98-100.
  7. H. Moon, On the invariant of Chen-Kuan for abelian varieties, Kyungpook Math. J., 56(3)(2016), 755-761. https://doi.org/10.5666/KMJ.2016.56.3.755
  8. J.-P. Serre, Abelian $\ell$-adic representations and elliptic curves, Lecture at McGill Uni-versity., W. A. Benjamin Inc., New York Amsterdam, 1968.