Korean J. Math.  Vol 25, No 2 (2017)  pp.137-145
DOI: http://dx.doi.org/10.11568/kjm.2017.25.2.137

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

Subject classification

11B05, 11J70, 11J71

Sponsor(s)

This work was supported by 2014 Hongik University Research Fund, NRF-2015R1D1A1A09059083, NRF-2009-0093827.

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References


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