On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus

Karin Halupczok

doi:10.5802/jtnb.666

Karin Halupczok

Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 1, pp. 203-213.

Résumé
Abstract

Pour $ε > 0$ et $n$ impair suffisamment grand, nous montrons que, pour presque tout $k \leq R : = n^{1 / 5 - ε}$ , 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 $k$ .

For $ε > 0$ and any sufficiently large odd $n$ we show that for almost all $k \leq R : = n^{1 / 5 - ε}$ 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 $k$ .

Publié le : 2009-08-24

MR 2537712 | Zbl pre05620677

DOI : https://doi.org/10.5802/jtnb.666

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

Karin Halupczok. On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus. Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 1, pp. 203-213. doi : 10.5802/jtnb.666. https://jtnb.centre-mersenne.org/item/JTNB_2009__21_1_203_0/

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