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Continued fractions and the density of graphs of some functions
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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.
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.
참고문헌 (6)
- H. Chae, "Equidistribution of higher dimensional generalized Dedekind sums and exponential sums"
- J. Lee, "Higher Hickerson formula", J. Number Theory, 170, pp.191~210 (2017)
- H. Davenport, "The distribution of quadratic and higher residues", Publ. Math. Debrecen, 2, pp.252~265 (1952)
- D. Hickerson, "Continued fractions and density results for Dedekind sums", J. Reine Angew. Math, 290, pp.113~116 (1977)
- H. Rademacher, "Dedekind sums", Carus Math. Monogr, 16 (1972), Math. Assoc. Amer.
- T. Tao, "Higher order Fourier analysis" (2012), Amer. Math. Soc
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