A lower bound on the mean value of the Erdős–Hooley Delta function

Abstract

Abstract We give an improved lower bound for the average of the Erdős–Hooley function , namely for all and any fixed , where is an exponent previously appearing in work of Green and the first two authors. This improves on a previous lower bound of of Hall and Tenenbaum, and can be compared to the recent upper bound of of the second and third authors.

Locations

• Proceedings of the London Mathematical Society - View - PDF
• Proceedings of the London Mathematical Society - View - PDF
• Proceedings of the London Mathematical Society - View - PDF