3 Excerpts

- Published 2011

Let K be a fixed number field, assumed to be Galois over Q. Let r and f be fixed integers with f positive. Given an elliptic curve E, defined over K, we consider the problem of counting the number of degree f prime ideals of K with trace of Frobenius equal to r. Except in the case f = 2, we show that “on average,” the number of such prime ideals with norm less than or equal to x satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors.

@inproceedings{Smith2011AverageFD,
title={Average Frobenius Distribution for Elliptic Curves Defined over Finite Galois Extensions of the Rationals},
author={Ethan Smith},
year={2011}
}