AVERAGE FROBENIUS DISTRIBUTION FOR INERTS IN Q(i)
نویسندگان
چکیده
Given an integer r, we consider the problem of enumerating the inert prime ideals p of Q(i) for which a given elliptic curve E has trace of Frobenius at p 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 LangTrotter conjecture for elliptic curves over Q.
منابع مشابه
Distribution of Farey Fractions in Residue Classes and Lang–Trotter Conjectures on Average
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