3-tuples have at most 7 prime factors infinitely often

James Maynard

doi:10.1017/S0305004113000339

paper

3-tuples have at most 7 prime factors infinitely often

arXiv:1205.5021 · doi:10.1017/S0305004113000339

Abstract

Let $L_{1}$ , $L_{2}$ $L_{3}$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_{1} (n) L_{2} (n) L_{3} (n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.

13 Pages

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