Products of primes in arithmetic progressions: a footnote in parity breaking
Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 219-225.

We prove that, if x and q⩽x 1/16 are two parameters, then for any invertible residue class a modulo q there exists a product of exactly three primes, each one below x 1/3 , that is congruent to a modulo q.

Nous montrons que, étant donnés x et q⩽x 1/16 , toute classe inversible a modulo q contient au moins un produit d’exactement trois nombres premiers, chacun étant inférieur ou égal à x 1/3 .

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Accepted:
Published online:
DOI: 10.5802/jtnb.1024
Classification: 11N13,  11A41,  11N37,  11B13
Keywords: Primes in arithmetic progressions, Least prime quadratic residue, Linnik’s Theorem 
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Olivier Ramaré; Aled Walker. Products of primes in arithmetic progressions: a footnote in parity breaking. Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 219-225. doi : 10.5802/jtnb.1024. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1024/

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