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On a result of Marshall Hall

Published online by Cambridge University Press:  26 February 2010

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Trinity College, Cambridge.
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Extract

Marshall Hall has proved that every real number is representable as the sum of two continued fractions with partial quotients at most 4. This implies that for any real β1, β2 there exists a real α such that

for all integers x > 0 and y, where C is a positive constant. In this note I prove a generalization to r numbers β2, …, βr. The case r = 2 implies a result similar to Marshall Hall's but with a larger number (71) in place of 4.

Type
Research Article
Information
Mathematika , Volume 3 , Issue 2 , December 1956 , pp. 109 - 110
Copyright
Copyright © University College London 1956

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References

* Annals of Math., 48 (1947), 966–993.CrossRefGoogle Scholar