TY - JOUR
T1 - On primitive points of elliptic curves with complex multiplication
AU - Chen, Yen Mei J.
AU - Yu, Jing
N1 - Funding Information:
Research partially supported by National Science Council, Republic of China. ∗Corresponding author. Department of Mathematics, National Central University, Taoyuan, Taiwan, ROC. E-mail addresses: [email protected] (Y.-M.J. Chen), [email protected] (J. Yu).
PY - 2005/9
Y1 - 2005/9
N2 - Let E be an elliptic curve defined over ℚ and P ∈ E(ℚ) a rational point of infinite order. Suppose that E has complex multiplication by an order in the imaginary quadratic field k. Denote by ME,P the set of rational primes ℓ such that ℓ splits in k, E has good reduction at ℓ, and P is a primitive point modulo ℓ. Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set ME,P explicitly.
AB - Let E be an elliptic curve defined over ℚ and P ∈ E(ℚ) a rational point of infinite order. Suppose that E has complex multiplication by an order in the imaginary quadratic field k. Denote by ME,P the set of rational primes ℓ such that ℓ splits in k, E has good reduction at ℓ, and P is a primitive point modulo ℓ. Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set ME,P explicitly.
KW - Complex multiplication
KW - Density
KW - Elliptic curves
KW - Primitive points
UR - http://www.scopus.com/inward/record.url?scp=23844492787&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2005.02.005
DO - 10.1016/j.jnt.2005.02.005
M3 - 期刊論文
AN - SCOPUS:23844492787
SN - 0022-314X
VL - 114
SP - 66
EP - 87
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -