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Simultaneous Diophantine Approximation

Published online by Cambridge University Press:  20 November 2018

Gordon Raisbeck
Gordon Raisbeck*
Affiliation:
Bell Telephone Laboratories, Murray Hill, N.J.
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Summary of results. The principal result of this paper is as follows: givenany set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that

(0.11).

Also, if n = 2, we can, given t, produce numbers z1 and z2 such that

(0.12)

This supersedes the results of Nils Pipping (Acta Aboensis, vol. 13, no. 9, 1942)that there is a q satisfying (0.11) such that , and also theclassical result of Dirichlet that there is such a q less than tn.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 283 - 288
Copyright
Copyright © Canadian Mathematical Society 1950

References

1 Here, exceptionally, t need not be an integer.