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

• Autorzy: J. Cheon , S. Hahn
• Języki publikacji: EN

Słowa kluczowe

EN

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

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 11G05: Elliptic curves over global fields
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 3
• Strony: 219-111

Daty

wydano

1999

otrzymano

1997-06-10

poprawiono

1998-10-26

Twórcy

autor

J. Cheon

• Section 0710, Electronics and Telecommunications Research Institute, Taejon 305-350, Republic of Korea

autor

S. Hahn

• Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Republic of Korea

Bibliografia

• [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 $A^n-B^n$ 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.