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On primitive points of elliptic curves with complex multiplication |
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| Authors: | Yen-Mei J Chen Jing Yu |
| Institution: | a Department of Mathematics, National Central University, Taoyuan, Taiwan, ROC b Department of Mathematics, National TsingHua University, HsinChu, Taiwan, ROC c National Center for Theoretical Sciences, Hsinchu, Taiwan, ROC |
| Abstract: | 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 ? such that ? splits in k, E has good reduction at ?, and P is a primitive point modulo ?. Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set ME,P explicitly. |
| Keywords: | 11G05 14K22 11R45 |
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