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On a theorem of P. J. Cohen

Published online by Cambridge University Press:  26 February 2010

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

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References

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

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