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On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums

Published online by Cambridge University Press:  24 October 2008

R. R. Hall  and
J. C. Wilson
R. R. Hall
Affiliation:
Department of Mathematics, University of York, York Y01 5DD
J. C. Wilson
Affiliation:
Department of Mathematics, University of York, York Y01 5DD
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Extract

A number of authors, including Apostol [1], Carlitz [2], Mikolás [5] and Rademacher [9] have obtained linear relations for the Dedekind sums

(the inhomogeneous sum) and the homogeneous sum

Here denotes the periodic extension into ℝ of the Bernoulli polynomial Bm(X) on [0, 1] given by the relation

with the exception that we define

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 9 - 24
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

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