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 qx 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 qx 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 .

Received:
Revised:
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
Ramaré, Olivier 1; Walker, Aled 2

1 CNRS / Institut de Mathématiques de Marseille Aix Marseille Université, U.M.R. 7373 Site Sud, Campus de Luminy, Case 907 13288 MARSEILLE Cedex 9, France
2 Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG, United Kingdom
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Ramaré, Olivier; Walker, Aled. 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. http://www.numdam.org/articles/10.5802/jtnb.1024/

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