The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve

J. Cheon; S. Hahn

Acta Arithmetica (1999)

  • Volume: 88, Issue: 3, page 219-111
  • ISSN: 0065-1036

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J. Cheon, and S. Hahn. "The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve." Acta Arithmetica 88.3 (1999): 219-111. <http://eudml.org/doc/207242>.

@article{J1999,
author = {J. Cheon, S. Hahn},
journal = {Acta Arithmetica},
keywords = {Bang's theorem; elliptic curves; reductions; local heights; Mordell-Weil groups; prime of good reduction},
language = {eng},
number = {3},
pages = {219-111},
title = {The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve},
url = {http://eudml.org/doc/207242},
volume = {88},
year = {1999},
}

TY - JOUR
AU - J. Cheon
AU - S. Hahn
TI - The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 3
SP - 219
EP - 111
LA - eng
KW - Bang's theorem; elliptic curves; reductions; local heights; Mordell-Weil groups; prime of good reduction
UR - http://eudml.org/doc/207242
ER -

References

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  1. [1] A. Bang, Taltheoretiske Undersøgelser, Tidsskr. Math. (5) 4 (1886), 70-80 and 130-137. 
  2. [2] Y. Ihara, On Fermat quotient and 'differentiation of numbers', RIMS Kokyuroku 810 (Algebraic Analysis and Number Theory) (1992), 324-341 (in Japanese). Zbl0966.11509
  3. [3] P. Ribenboim, Catalan's Conjecture, Academic Press, 1994. Zbl0824.11010
  4. [4] A. Schinzel, Primitive divisors of the expression A n - B n in algebraic number fields, J. Reine Angew. Math. 268 (1974), 27-33. Zbl0287.12014
  5. [5] J. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
  6. [6] J. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. Zbl0729.14026
  7. [7] J. Silverman, Wieferich's criterion and the abc-conjecture, J. Number Theory 30 (1988), 226-237. Zbl0654.10019
  8. [8] K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892), 265-284. 

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