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Some Diophantine inequalities

Published online by Cambridge University Press:  26 February 2010

L. J. Mordell
L. J. Mordell
Affiliation:
University of Toronto, Canada, and St. John's College, Cambridge.
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Extract

Let →(X) be a function of the n variables (X) = (X1, …, Xn) defined for all real (X). A fundamental problem in the theory of Diophantine approximation is to prove the existence of real numbers (X) ≡ (x) (mod 1), where (x) = (x1, …, xn) is any given set of real numbers, for which

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Type
Research Article
Information
Mathematika , Volume 2 , Issue 2 , December 1955 , pp. 145 - 149
Copyright
Copyright © University College London 1955

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References

* See Swinnerton-Dyer, H. P. F., Proc. Cambridge Phil. Soc., 50 (1954), 209–219CrossRefGoogle Scholar, Lemma (§4), and a paper by Birch and Swinnerton-Dyer to appear in Mathematika.