Goldbach's conjecture in arithmetic progressions: number and size of exceptional prime moduli

摘要

Set T = N1/3 - epsilon. It is proved that for all but "TL-H, H > 0, exceptional prime numbers k = T and almost all integers b(1), b(2) co-prime to k, almost all integers n similar to N satisfying n = b(1) + b(2)(mod k) can be written as the sum of two primes p(1) and p(2) satisfying p(i) = b(i)(mod k),i = 1, 2. For prime numbers k = N5/24-epsilon, this result is even true for all but "(log N)(D) primes k and all integers b(1), b(2) co-prime to k.