Average twin prime conjecture for elliptic curves

摘要

Let E be an elliptic curve over ?. In 1988, N. 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 F{double-struck}_p is prime. This is an analogue of the Hardy-Littlewood twin prime conjecture in the case of elliptic curves.