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LINES FULL OF DEDEKIND SUMS

Published online by Cambridge University Press:  14 June 2004

G. MYERSON  and
N. PHILLIPS
G. MYERSON
Affiliation:
Mathematics, Macquarie University, NSW 2109, Australiagerry@maths.mq.edu.au
N. PHILLIPS
Affiliation:
130 Herring Road, North Ryde, NSW 2113, Australianicko_phillo@yahoo.com.au
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Abstract

Let $s:\Q\,{\longrightarrow}\,\Q$ be the Dedekind sum, given by $s(h/k)=\sum_{\nu=1}^{k-1}({\nu/k}\,{-}\,{1/2})(\{{h\nu/k}\}\,{-}\,{1/2})$ when $\gcd(h,k)\,{=}\,1$. Then for every rational $\alpha\,{\ne}\,1/12$ there are infinitely many rational $x$ such that $s(x)\,{=}\,\alpha x$. Also, the fixed points of $s$ are dense in the real line.

Keywords

11F20
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 4 , July 2004 , pp. 547 - 552
Copyright
© The London Mathematical Society 2004

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