Reducing the number of prime factors of long $\kappa$-tuples

Name: Reducing the number of prime factors of long $\kappa$-tuples
Creator: Franze, C. S.
Keywords: Mathematics - Number Theory, 11N35, 11N36, 0101 mathematics, 01 natural sciences

Franze, C. S.

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Reducing the number of prime factors of long $\kappa$-tuples

descriptionPublicationkeyboard_double_arrow_right Preprint 08 Nov 2011

Authors: Franze, C. S.;

arXiv: 1111.2003

Reducing the number of prime factors of long $\kappa$-tuples

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Abstract

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.

Comment: 15 pages, submitted to London Mathematical Society

Keywords

Mathematics - Number Theory, 11N35, 11N36

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