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- W2766135633 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." @default.
- W2766135633 created "2017-11-10" @default.
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- W2766135633 date "2018-04-01" @default.
- W2766135633 modified "2023-09-29" @default.
- W2766135633 title "Koblitz's conjecture on average for elliptic curves over abelian number fields of square-free conductor" @default.
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- W2766135633 doi "https://doi.org/10.1016/j.jnt.2017.09.013" @default.
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