On primitive points of elliptic curves with complex multiplication

被引：2
|
作者：
Chen, YMJ [1 ]
Yu, J
机构：
[1] Natl Cent Univ, Dept Math, Taoyuan, Taiwan
[2] Natl Tsing Hua Univ, Dept Math, Hsinchu, Taiwan
[3] Natl Ctr Theoret Sci, Hsinchu, Taiwan
来源：
JOURNAL OF NUMBER THEORY | 2005年 / 114卷 / 01期
关键词：
primitive points; elliptic curves; complex multiplication; density;
D O I：
10.1016/j.jnt.2005.02.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let E be an elliptic curve defined over Q and P is an element of 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 M-E,M-P explicitly. (c) 2005 Elsevier Inc. All rights reserved.
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页码：66 / 87
页数：22
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