Products of primes in arithmetic progressions: a footnote in parity breaking

Olivier Ramaré; Aled Walker

Products of primes in arithmetic progressions: a footnote in parity breaking

Number Theory 2019-03-04 v2

Authors: Olivier Ramaré , Aled Walker

Abstract

We prove that, if $x$ and $q\leqslant x^{1/16}$ 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 $q$ .

Keywords

products of primes arithmetic progressions parity breaking invertible residue class modular congruence number theory

Cite

@article{arxiv.1610.05804,
  title  = {Products of primes in arithmetic progressions: a footnote in parity breaking},
  author = {Olivier Ramaré and Aled Walker},
  journal= {arXiv preprint arXiv:1610.05804},
  year   = {2019}
}

Comments

6 pages, to submitted to Journal de Th\'{e}orie des Nombres de Bordeaux. Small corrections to previous version

Products of primes in arithmetic progressions: a footnote in parity breaking

Abstract

Keywords

Cite

Comments

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