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Continued fractions and the density of graphs of some functions
채희준,전병흡,이정연 강원경기수학회 2017 한국수학논문집 Vol.25 No.2
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.
Equidistribution of higher dimensional generalized Dedekind sums and exponential sums
채희준,전병흡,Jungyun Lee 대한수학회 2020 대한수학회지 Vol.57 No.4
We consider generalized Dedekind sums in dimension $n$, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in $\FR/\FZ$.
MOTIVICITY OF THE MIXED HODGE STRUCTURE OF SOME DEGENERATIONS OF CURVES
채희준,전병흡 대한수학회 2010 대한수학회보 Vol.47 No.3
We consider a degeneration of genus 2 curves, which is opposite to maximal degeneration in a sense. Such a degeneration of curves yields a variation of mixed Hodge structure with monodromy weight filtration. The mixed Hodge structure at each fibre, which is different from the limit mixed Hodge structure of Schmid and Steenbrink, can be realized as H1 of a noncompact singular elliptic curve. We also prove that the pull back of the above variation of mixed Hodge structure to a double cover of the base space comes from a family of noncompact singular elliptic curves.