In this paper, we consider the mean value of the product of two real valued multiplicative functions with shifted arguments. The functions F and G under consideration are close to two nicely behaved functions A and B, such that the average value of A(. n-. h). B(. n) over any arithmetic progression is only dependent on the common difference of the progression. We use this method on the problem of finding mean value of NK(. N)/ϕ(. N), where NK(. N)/ϕ(. N)log N is the expected number of primes such that a random elliptic curve over rationals has N points when reduced over those primes.
- Asymptotic of mean value
- Elliptic curve over finite fields
- Shifted multiplicative function