Reducing the number of prime factors of long $κ$-tuples

Details Reducing the number of prime factors of long $κ$-tuples Reducing the number of prime factors of long $κ$-tuples

2011-11-08

arxiv.org/abs/1111.2003v1

Mathematics

Number Theory

15 pages, submitted to London Mathematical Society

Scientific paper

We prove that there are infinitely many integers $n$ such that the total
number of prime factors of $(n+h_{1})(n+h_{2})...(n+h_{\kappa})$ is at most
$(1/2)\kappa\log\kappa+O(\kappa)$, provided $\kappa$ is sufficiently large.

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