DOI: https://doi.org/10.11568/kjm.2017.25.2.137

### Continued fractions and the density of graphs of some functions

#### 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

#### Subject classification

11B05, 11J70, 11J71#### Sponsor(s)

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

PDF#### References

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