The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
Tom 159 / 2013
Acta Arithmetica 159 (2013), 227-243
MSC: 11F32, 11F25.
DOI: 10.4064/aa159-3-2
Streszczenie
It is proved that for almost all prime numbers any fixed integer b_{2}, (b_{2},k)=1, and almost all integers b_{1}, 1\leq b_{1}\leq k, (b_{1},k)=1, almost all integers n satisfying n\equiv b_{1}+b_{2}\,\, ({\rm mod}\,\, k) can be written as the sum of two primes p_{1} and p_{2} satisfying p_{i}\equiv b_{i}\,\,({\rm mod}\,\, k), i=1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.