Korean Journal of Mathematics

  • 제25권2호
  • /
  • Pages.137-145
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  • 2017
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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CONTINUED FRACTIONS AND THE DENSITY OF GRAPHS OF SOME FUNCTIONS

  • Chae, Hi-joon (Department of Mathematics Education Hongik University) ;
  • Jun, Byungheup (Department of Mathematical Sciences UNIST) ;
  • Lee, Jungyun (Department of Mathematics Ewha Womans University)
  • 투고 : 2017.01.17
  • 심사 : 2017.03.30
  • 발행 : 2017.06.30
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초록

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

  1. H. Chae, B. Jun and J. Lee, Equidistribution of higher dimensional generalized Dedekind sums and exponential sums, Submitted.
  2. J. Lee, B. Jun and H. Chae, Higher Hickerson formula, J. Number Theory 170 (2017), 191-210. https://doi.org/10.1016/j.jnt.2016.06.003
  3. H. Davenport and P. Erdos, The distribution of quadratic and higher residues, Publ. Math. Debrecen 2 (1952), 252-265.
  4. D. Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113-116.
  5. H. Rademacher and E. Grosswald, Dedekind sums, Carus Math. Monogr. 16, Math. Assoc. Amer., 1972.
  6. T. Tao, Higher order Fourier analysis, Graduate Studies in Mathematics 142, Amer. Math. Soc., 2012.

피인용 문헌

  1. THE SEQUENTIAL ATTAINABILITY AND ATTAINABLE ACE vol.26, pp.4, 2018, https://doi.org/10.11568/kjm.2018.26.4.757