Continued fractions and the density of graphs of some functions

Hi-joon Chae, Byungheup Jun, Jungyun Lee

Abstract


We consider some simple periodic functions on the field of rational numbers with values in $\mathbb{Q}/\mathbb{Z}$ which are defined in terms of lowest-term-expression of rational numbers. We prove the density of graphs of these functions by constructing explicitly points on the graphs close to a given point using continued fractions.


Keywords


continued fractions, Dedekind sums

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References


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DOI: http://dx.doi.org/10.11568/kjm.2017.25.2.137

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