The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
Acta Arithmetica, Tome 159 (2013) no. 3, pp. 227-243
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Claus Bauer 1 ; Yonghui Wang 2
@article{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},
pages = {227--243},
publisher = {mathdoc},
volume = {159},
number = {3},
year = {2013},
doi = {10.4064/aa159-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa159-3-2/}
}
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%0 Journal Article %A Claus Bauer %A Yonghui Wang %T The binary Goldbach conjecture with primes in arithmetic progressions with large modulus %J Acta Arithmetica %D 2013 %P 227-243 %V 159 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa159-3-2/ %R 10.4064/aa159-3-2 %G en %F 10_4064_aa159_3_2
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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