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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.
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참고문헌 (6)
참고문헌 신청
H. Chae / Equidistribution of higher dimensional generalized Dedekind sums and exponential sums
J. Lee / 2017 / Higher Hickerson formula / J. Number Theory 170:191~210
H. Davenport / 1952 / The distribution of quadratic and higher residues / Publ. Math. Debrecen 2:252~265
D. Hickerson / 1977 / Continued fractions and density results for Dedekind sums / J. Reine Angew. Math 290:113~116
H. Rademacher / 1972 / Dedekind sums / Carus Math. Monogr 16
J. Lee / 2017 / Higher Hickerson formula / J. Number Theory 170:191~210
H. Davenport / 1952 / The distribution of quadratic and higher residues / Publ. Math. Debrecen 2:252~265
D. Hickerson / 1977 / Continued fractions and density results for Dedekind sums / J. Reine Angew. Math 290:113~116
H. Rademacher / 1972 / Dedekind sums / Carus Math. Monogr 16
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