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Note on an identity connected with diophantine approximation

Published online by Cambridge University Press:  24 October 2008

H. Davenport
H. Davenport
Affiliation:
Trinity College
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Extract

In discussing Hecke's function

where {t} = t − [t] − ½ Hardy and Littlewood* made use of the identity

Here

θ is an irrational number between 0 and 1, and pν/qν is the νth convergent to θ (beginning with p0 = 0, q0 = 1). The proof of (1) given by Hardy and Littlewood is of an analytic character.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 1 , January 1938 , pp. 27
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* Hambury Abh. 3 (1923), 57–68.Google Scholar