Primes in arithmetic progressions to spaced moduli

摘要

Let A be the von Mangoldt function. For (a, q) = 1, let Σn≤xn≡a(nodq)Λ(n)=x/Φ(q)+E(x;q,a) It is well known that for given A > 0, C > 0,E(x;q):=max(a,q)=1|E(x;q,a)|《x/q(logx)~A for x > 2, q < (logX)~C . See e.g. Davenport [5].