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

Claus Bauer, and Yonghui Wang. "The binary Goldbach conjecture with primes in arithmetic progressions with large modulus." Acta Arithmetica 159.3 (2013): 227-243. <http://eudml.org/doc/279533>.

@article{ClausBauer2013,
abstract = {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 $p_\{i\} ≡ b_\{i\}(mod k)$, i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.},
author = {Claus Bauer, Yonghui Wang},
journal = {Acta Arithmetica},
keywords = {additive number theory; prime numbers; exponential sums},
language = {eng},
number = {3},
pages = {227-243},
title = {The binary Goldbach conjecture with primes in arithmetic progressions with large modulus},
url = {http://eudml.org/doc/279533},
volume = {159},
year = {2013},
}

TY - JOUR
AU - Claus Bauer
AU - Yonghui Wang
TI - The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
JO - Acta Arithmetica
PY - 2013
VL - 159
IS - 3
SP - 227
EP - 243
AB - 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 $p_{i} ≡ b_{i}(mod k)$, i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.
LA - eng
KW - additive number theory; prime numbers; exponential sums
UR - http://eudml.org/doc/279533
ER -