It is proved that for almost all prime numbers , 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 , i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-3-2,
author = {Claus Bauer and Yonghui Wang},
title = {The binary Goldbach conjecture with primes in arithmetic progressions with large modulus},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {227-243},
zbl = {06177629},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-3-2}
}
Claus Bauer; Yonghui Wang. The binary Goldbach conjecture with primes in arithmetic progressions with large modulus. Acta Arithmetica, Tome 161 (2013) pp. 227-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-3-2/