Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Abstract
© Cambridge Philosophical Society 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.
This paper has been withdrawn.