ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Section 0710, Electronics and Telecommunications Research Institute, Taejon 305-350, Republic of Korea
  2. Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Republic of Korea

Keywords

Bang's theorem, elliptic curves, reductions, local heights

Bibliography

  1. A. Bang, Taltheoretiske Undersøgelser, Tidsskr. Math. (5) 4 (1886), 70-80 and 130-137.
  2. Y. Ihara, On Fermat quotient and 'differentiation of numbers', RIMS Kokyuroku 810 (Algebraic Analysis and Number Theory) (1992), 324-341 (in Japanese).
  3. P. Ribenboim, Catalan's Conjecture, Academic Press, 1994.
  4. A. Schinzel, Primitive divisors of the expression An-Bn in algebraic number fields, J. Reine Angew. Math. 268 (1974), 27-33.
  5. J. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
  6. J. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  7. J. Silverman, Wieferich's criterion and the abc-conjecture, J. Number Theory 30 (1988), 226-237.
  8. K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892), 265-284.
Pages:
219-111
Main language of publication
English
Received
1997-06-10
Accepted
1998-10-26
Published
1999
Exact and natural sciences