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The binary Goldbach conjecture with primes in arithmetic progressions with large modulus

Claus BauerYonghui Wang — 2013

Acta Arithmetica

It is proved that for almost all prime numbers k N 1 / 4 - ϵ , any fixed integer b₂, (b₂,k) = 1, and almost all integers b₁, 1 ≤ b₁ ≤ k, (b₁,k) = 1, almost all integers n satisfying n ≡ b₁ + b₂ (mod k) can be written as the sum of two primes p₁ and p₂ satisfying p i b i ( m o d k ) , i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.

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