Battista, Jonathan; Bayless, Jonathan; Ivanov, Dmitriy; James, Kevin Average Frobenius distributions for elliptic curves with nontrivial rational torsion. (English) Zbl 1151.11022 Acta Arith. 119, No. 1, 81-91 (2005). Summary: Let \(E/{\mathbb Q}\) denote an elliptic curve, let \(a_p(E) = p+1-\#E({\mathbb F}_p)\) and for \(r\in {\mathbb Z}\), let \(\pi_E^r(X) := \#\{p \leq X : a_p(E) = r\}\). Lang and Trotter have conjectured that \(\pi_E^r(X) \sim C_{E,r} \frac{\sqrt{X}}{\log{X}}\), where \(C_{E,r}\) is an explicit constant depending only on \(E\) and \(r\). In this paper we consider the Lang-Trotter conjecture 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. Cited in 7 Documents MSC: 11G05 Elliptic curves over global fields 11F80 Galois representations PDFBibTeX XMLCite \textit{J. Battista} et al., Acta Arith. 119, No. 1, 81--91 (2005; Zbl 1151.11022) Full Text: DOI