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

Halupczok, Karin

doi:10.5802/jtnb.666

Halupczok, Karin ¹

¹ Albert-Ludwigs-Universität Freiburg Eckerstr. 1 D-79104 Freiburg, Allemagne

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 $k$ .

MR | 1 citation dans Numdam

DOI : 10.5802/jtnb.666

Affiliations des auteurs :

Halupczok, Karin ¹

¹ Albert-Ludwigs-Universität Freiburg Eckerstr. 1 D-79104 Freiburg, Allemagne

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     title = {On the ternary {Goldbach} problem with primes in arithmetic progressions having a common modulus},
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     publisher = {Universit\'e Bordeaux 1},
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Halupczok, Karin. 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. http://www.numdam.org/articles/10.5802/jtnb.666/

Bibliographie
Cité par

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