Title

Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals

Document Type

Article

Publication Date

2-1-2018

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.

Publication Title

Journal of the Institute of Mathematics of Jussieu

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