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A sequence well distributed in the square

Published online by Cambridge University Press:  24 October 2008

R. G. E. Pinch
R. G. E. Pinch
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
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Extract

Bollobás and Erdös[1] have posed the problem:

If a is irrational, show that for 1 ≤ i < j ≤ p the number of integers t with 1 ≤ t ≤ p such that {(t–i)2a} < d and {(t–j)2a} < d, 0 < d < 1, is d2p + o(p) uniformly in i, j.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 19 - 22
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Bollobás, B. and Erdös, P.. An extremal problem of graphs with diameter 2. Mathematics Magazine 48 (1975), 281–283.CrossRefGoogle Scholar
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[4]Kuipers, L. and Niederreiter, H.. Uniform Distribution of Sequences (Wiley, 1974).Google Scholar
[5]Weyl, H.. Uber die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77 (1916), 313–352.CrossRefGoogle Scholar