Geodesic
The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
Claus Bauer 1   ; Yonghui Wang 2
1 Dolby Laboratories Beijing 100020, P.R. China
2 Department of Mathematics Capital Normal University Xi San Huan Beilu 105 Beijing 100048, P.R. China
Acta Arithmetica, Tome 159 (2013) no. 3, pp. 227-243 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is proved that for almost all prime numbers $k\leq N^{1/4-\epsilon},$ 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.
DOI : 10.4064/aa159-3-2
Keywords: proved almost prime numbers leq epsilon fixed integer almost integers leq leq almost integers satisfying equiv mod written sum primes satisfying equiv mod proof result estimates exponential sums primes arithmetic progressions derived

Claus Bauer  1   ; Yonghui Wang  2

1 Dolby Laboratories Beijing 100020, P.R. China
2 Department of Mathematics Capital Normal University Xi San Huan Beilu 105 Beijing 100048, P.R. China 
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     title = {The binary {Goldbach} conjecture with primes in arithmetic progressions with large modulus},
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Claus Bauer; Yonghui Wang. The binary Goldbach conjecture with primes in arithmetic progressions with large modulus. Acta Arithmetica, Tome 159 (2013) no. 3, pp. 227-243. doi: 10.4064/aa159-3-2

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