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3-tuples have at most 7 prime factors infinitely often

Published online by Cambridge University Press:  18 June 2013

JAMES MAYNARD
JAMES MAYNARD*
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB. email: maynard@maths.ox.ac.uk
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Abstract

Let L1, L2L3 be integer linear functions with no fixed prime divisor. We show there are infinitely many n for which the product L1(n)L2(n)L3(n) has at most 7 prime factors, improving a result of Porter from 1972. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 443 - 457
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

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