• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.559-578
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• 2019

We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.595-606
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• 2001

Using p-adic class number formula, we derive a congru-ence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowlas theo-rem, Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.315-323
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• 2023

First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-89
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• 1998

Using the list of all imaginary quadratic fields with class number 1, 2, 3 and 6, we determine all imaginary bicyclic biquadratic number fields of class number 3. There are exactly 163 such fields and their conductors are less than or equal to 163 $\cdot$883.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.907-928
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• 2015

We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.163-171
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• 2007

In this paper, we determine all subfields of cyclotomic function fields with divisor class number two. We also give the generators of such fields explicitly.

• Journal of the Korean Society of Safety
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• v.32 no.5
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• pp.88-95
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• 2017

As the safety fields are expanding to a variety of industrial fields, safety technology has been developed by convergence between industrial safety fields such as mechanics, ergonomics, electronics, chemistry, construction, and information science. As the technology convergence is facilitating recently advanced safety technology, it is important to explore the trends of safety technology for understanding which industrial technologies have been integrated thus far. For studying the trends of technology, the patent is considered one of the useful sources that has provided the ample information of new technology. The patent has been also used to identify the patterns of technology convergence through various quantitative methods. In this respect, this study aims to identify the convergence patterns and fields of safety technology using association rule mining(ARM)-based patent co-classification(co-class) analysis. The patent co-class data is especially useful for constructing convergence network between technological fields. Through linkages between technological fields, the core and hub classes of convergence network are explored to provide insight into the fields of safety technology. As the representative method for analyzing patent co-class network, the ARM is used to find the likelihood of co-occurrence of patent classes and the ARM network is presented to visualize the convergence network of safety technology. As a result, we find three major convergence fields of safety technology: working safety, medical safety, and vehicle safety.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.517-523
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• 2013

In this paper we study the infiniteness of Hilbert 3-class field tower of real cubic function fields over $\mathbb{F}_q(T)$, where $q{\equiv}1$ mod 3. We also give various examples of real cubic function fields whose Hilbert 3-class field tower is infinite.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.