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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Diophantine approximation properties of certain infinite sets


Author: Wolfgang M. Schmidt
Journal: Trans. Amer. Math. Soc. 278 (1983), 635-645
MSC: Primary 10F10; Secondary 10K15
MathSciNet review: 701515
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Abstract: We exhibit various infinite sets of reals whose finite subsets do not have good simultaneous rational approximations. In particular there is an infinite set such that each finite subset is "badly approximable" in the sense that Dirichlet's theorem is best possible up to a multiplicative constant.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0701515-3
Article copyright: © Copyright 1983 American Mathematical Society