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    Title: On a density problem for elliptic curves over finite fields
    Authors: Chen, Yen-mei J.;Yu, Jing
    Contributors: 淡江大學數學學系
    Date: 2000-12-01
    Issue Date: 2010-01-28
    Publisher: Somerville, MA: International Press
    Abstract: We prove an analogue of Artin’s primitive root conjecture for two-dimensional tori ResK/Q Gm under the Generalized Riemann Hypothesis, where K is an imaginary quadratic field. As a consequence, we are able to derive a precise density formula for a given elliptic curve E over a finite prime field. One adjoins coordinates of all `-torsion points to the base field and asks for the density of the rational primes ` for which the resulting Galois extension over the base field has degree ` 2 − 1. It turns out that the density in question is essentially independent of the curves, and unless in certain special cases, even independent of the characteristic p if p 6≡ 1 (mod 4).
    Relation: The Asia Journal of Mathematics 4(4), pp.737-756
    DOI: 10.4310/AJM.2000.v4.n4.a2
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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