Twins of s-free numbers

Abstract

We generalise the square sieve developed by Heath-Brown to higher powers in order to improve on the error term for the problem of counting consecutive power-free numbers.

This work has been submitted as a Diploma Thesis to the University of Stuttgart in 2009 essentially in its current form, and is now being made available as interest in this and related problems seems to have recently increased. One should note that the main result has since been improved by Reuss (arXiv:1212.3150) and by forthcoming work of Dietmann and Marmon; Diplomarbeit, Universität Stuttgart, 2009

Cited by in corpus (3)

• The density of twins of $k$-free numbers
• Moments of the distribution of $k$-free numbers in short intervals and arithmetic progressions
• Configurations Of Consecutive Primitive Roots