Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Copyright © 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.
Mathematical Proceedings of the Cambridge Philosophical Society
Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals.
Mathematical Proceedings of the Cambridge Philosophical Society,
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