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On a theorem of Beck

Published online by Cambridge University Press:  18 May 2009

K. F. Roth
K. F. Roth
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, 179–180 Queen's Gate London SW7 2BZ
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Let T(N) be the least integer such that one can assign ±l's to any N points in the unit square so that the sum of these values in any rectangle with sides parallel to those of the square have absolute value at most T(N). In [1] Beck showed, among other results, that (for N≥2)

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Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 195 - 201
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Beck, József, Balanced Two-Colorings of Finite Sets in the Square I, Combinatorica 1 (1981), 327–335.CrossRefGoogle Scholar
2.Schmidt, W. M., Irregularities of Distribution VII, Acta Arith., 21 (1972), 45–50.CrossRefGoogle Scholar
3.Schmidt, W. M., Irregularities of Distribution X, Number Theory and Algebra (ed. Zassenhaus, H., Academic Press, 1977), 311–329.Google Scholar
4.Halász, G., On Roth's method in the theory of irregularities of point distributions, Recent Progress in Analytic Number Theory, Vol. 2 (eds. Halberstam, H. and Hooley, C., Academic Press, 1981), 79–94.Google Scholar