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Average Frobenius Distribution for Inerts in β(i)
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Given an integer r, we consider the problem of enumerating the inert prime ideals π of β(i) for which a given elliptic curve E has trace of Frobenius atΒ π equal to r. We prove that on average the number of such prime ideals up to x is asymptotic to cr log log x where cr is an explicit constant computed in terms of an Euler product. This result is in accordance with the standard heuristics. This problem generalises naturally the classical Lang-Trotter conjecture for elliptic curves over β.
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