The Average Rank of an Algebraic Family of Elliptic Curves
نویسندگان
چکیده
Let E=Q(T) be a one-parameter family of elliptic curves. Assuming various standard conjectures, we give an upper bound for the average rank of the bers E t (Q) with t 2 Z, improving earlier estimates of Fouvry-Pomykala and Michel. We also show how certain assumptions about the distribution of zeros of L-series might help explain the experimentally observed fact that the average rank of the bers appears to be strictly larger than the naive expected value of rank E(Q(T)) + 1=2.
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تاریخ انتشار 1997