The “Density” of the Zeros of Dirichlet L-Series and the Problem of the Sum of Primes and “Near Primes”

Let π(x, D, ℓ) denote the number of primes in (1, x) which are ≡ ℓ(mod D). In this paper, a mean value theorem on π(x, D, ℓ) for (ℓ, D) =1 and “almost” all D ≤ x^{3/8 - ε} is proved, where ε is any pre-assigned positive number…