Continued fractions and the density of graphs of some functions

Hi-joon Chae, Byungheup Jun, Jungyun Lee


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.


continued fractions, Dedekind sums

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