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An analogue of a problem of Littlewood

Published online by Cambridge University Press:  26 February 2010

J. V. Armitage
J. V. Armitage
Affiliation:
Department of Mathematics, King's College London, Strand, London, W.C.2.
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Extract

Littlewood posed the following problem: for each pair of real numbers, θ and φ, and each ε > 0, is there a positive integer n such that

where ‖α‖ denotes the difference between a and the nearest integer.

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 101 - 105
Copyright
Copyright © University College London 1969

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References

1.Baker, A., “On an analogue of Littlewood's diophantine approximation problem”, Michigan Math. J., 11 (1964), 247–250.CrossRefGoogle Scholar
2.Cusick, T. W., Ph.D. Dissertation (University of Cambridge, 1967).Google Scholar
3.Davenport, H. and Lewis, D. J., “An analogue of a problem of Littlewood”, Michigan Math. J., 10 (1963), 157–160.CrossRefGoogle Scholar
4.Kaplansky, I., An introduction to differential algebra (Hermann, Paris, 1957).Google Scholar