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Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Published online by Cambridge University Press: 15 March 2011
Abstract
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 3 , May 2011 , pp. 439 - 458
- Copyright
- Copyright © Cambridge Philosophical Society 2011
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