Average Frobenius Distributions for Elliptic Curves with 3-torsion
نویسنده
چکیده
In this paper, we examine the Lang-Trotter conjecture for elliptic curves which possess rational 3-torsion points. We prove that if one averages over all such elliptic curves then one obtains an asymptotic similar to the one predicted by Lang and Trotter.
منابع مشابه
To appear in Acta Arithmetica. AVERAGE FROBENIUS DISTRIBUTIONS FOR ELLIPTIC CURVES WITH NONTRIVIAL RATIONAL TORSION
In this paper we consider the Lang-Trotter conjecture (Conjecture 1 below) for various families of elliptic curves with prescribed torsion structure. We prove that the Lang-Trotter conjecture holds in an average sense for these families of curves (see Theorem 3). Let E/Q denote an elliptic curve and let ∆E denote its discriminant. As usual, let ap(E) = p + 1 − #E(Fp). Then we have the following...
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تاریخ انتشار 2005