Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T12:48:24.868Z Has data issue: false hasContentIssue false
  • English
  • Français

On a theorem of P. J. Cohen

Published online by Cambridge University Press:  26 February 2010

H. Davenport
H. Davenport
Affiliation:
Trinity College, Cambridge.
Get access

Extract

Let N be a large positive integer and let n1, …, nN be any N distinct integers. Let

Hardy and Littlewood proposed the problem: to find a lower bound for

in terms of N, this lower bound to be a function of N which tends to infinity with N. It is easily seen, on examining the case when n1, …, nN art in arithmetic progression, that a lower bound of higher order than log N is impossible.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 2 , December 1960 , pp. 93 - 97
Copyright
Copyright © University College London 1960

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

† J. London Math. Soc., 23 (1948), 163–168 (see p.168).Google Scholar

‡ American J. of Math., 82 (1960), 191–212CrossRefGoogle Scholar