most citedAverage twin prime conjecture for elliptic curves

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math.NT2007★ 5 cited

Average twin prime conjecture for elliptic curves

Antal Balog, Alina Cojocaru, Chantal David

Let E be an elliptic curve over Q. In 1988, Koblitz conjectured a precise asymptotic for the number of primes p up to x such that the order of the group of points of E over the fin…

math.NT2007

Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

A. C. Cojocaru, I. E. Shparlinski

We prove that the set of Farey fractions of order , that is, the set $\{α/β\in \Q : \gcd(α, β) = 1, 1 \le α, β\le T\}$, is uniformly distributed in residue classes modulo a prim…