Abstract
Let E be a rational elliptic curve defined over the rational numbers. For a prime of good reduction p of E, let #E(Fp) denote the number of Fp-rational solutions on the reduction of E modulo p. In 1988, Koblitz conjectured that for any real number x#{p<x:p prime and #E(Fp) prime}∼CE⋅xlog2x, where CE is an explicit constant. Balog, Cojocaru, and David recently proved that Koblitz's conjecture is true on average for rational elliptic curves. In this paper we generalize their result to elliptic curves over any abelian number field with square-free conductor.
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