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Some metrical theorems in Diophantine approximation. III†

Published online by Cambridge University Press:  24 October 2008

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Trinity CollegeCambridge
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Extract

Let

be w sequences of differentiable functions defined in the ranges

where aj, bj may be − ∞, + ∞ respectively. For each j and each m ≠ n let

be monotonic and let there be a constant K independent of m, n, j, θj such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 2 , April 1950 , pp. 219 - 225
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

REFERENCES

(1)Drewes, A. ‘Diophantische Benaderingsproblemen.’ Dissertation, Amsterdam, 1945, especially Hoofstuk II, Stelling 2 (p. 19).Google Scholar
(2)Fowler, R. H.On the distribution of the sets of points (λn θ). Proc. London Math. Soc. (2), 14 (1914–1915), 189–206.Google Scholar
(3)Khintchine, A.Ein Satz über Kettenbrüche mit arithmetischen Anwendungen. Math. Z. 18 (1923), 289–306.CrossRefGoogle Scholar
(4)Khintchine, A.Ueber einem Satz der Wahrscheinlichkeitsrechnung. Fund. Math. 6 (1924), 9–20.CrossRefGoogle Scholar
(5)Koksma, J. F.Metrisches zur Theorie der Diophantischen Approximationen. Proc. K. Akad. Wet. Amsterdam, 39 (1936), 225–40.Google Scholar
(6)Weyl, H.Ueber die Gleichverteilung von Zahlen mod Eins. Math. Ann. 77 (1915–1916), 313–52.CrossRefGoogle Scholar