On numbers with many rational approximations
Published online by Cambridge University Press: 24 October 2008
Extract
Every real number α admits many rational approximations in the sense that for every natural number q,
for some integer p. Perhaps surprisingly, numbers α which have k distinct rational approximations with given denominators q1,…,qk,
for a fixed ε > 0, are quite sparse; their measure in U = [0,1) is at most C(ε)/k.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 25 - 27
- Copyright
- Copyright © Cambridge Philosophical Society 1979
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