On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 1, p. 203-213

For $\epsilon >0$ and any sufficiently large odd $n$ we show that for almost all $k\le R:={n}^{1/5-\epsilon }$ there exists a representation $n={p}_{1}+{p}_{2}+{p}_{3}$ with primes ${p}_{i}\equiv {b}_{i}$ mod $k$ for almost all admissible triplets ${b}_{1},{b}_{2},{b}_{3}$ of reduced residues mod $k$.

Pour $\epsilon >0$ et $n$ impair suffisamment grand, nous montrons que, pour presque tout $k\le R:={n}^{1/5-\epsilon }$, il existe une représentation $n={p}_{1}+{p}_{2}+{p}_{3}$ avec des nombres premiers ${p}_{i}\equiv {b}_{i}$ modulo $k$ pour presque tout triplet admissible ${b}_{1},{b}_{2},{b}_{3}$ de résidus modulo $k$.

@article{JTNB_2009__21_1_203_0,
author = {Halupczok, Karin},
title = {On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus},
journal = {Journal de th\'eorie des nombres de Bordeaux},
publisher = {Universit\'e Bordeaux 1},
volume = {21},
number = {1},
year = {2009},
pages = {203-213},
doi = {10.5802/jtnb.666},
mrnumber = {2537712},
zbl = {pre05620677},
language = {en},
url = {http://www.numdam.org/item/JTNB_2009__21_1_203_0}
}

Halupczok, Karin. On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 1, pp. 203-213. doi : 10.5802/jtnb.666. http://www.numdam.org/item/JTNB_2009__21_1_203_0/

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