• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.455-464
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• 2012

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

• 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 Chungcheong Mathematical Society
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• v.29 no.1
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• pp.117-121
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• 2016

In this paper we give a determinant formula for the ratio of relative congruence zeta functions of cyclotomic function fields.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.83-88
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• 2015

In this paper we give a determinant formula for the relative congruent zeta function in cyclotomic function fields.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.735-740
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• 2013

In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.259-273
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• 2005

In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.553-562
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• 2014

In this paper we study of densities of the 4-rank of narrow ideal class groups of real quadratic function fields over the rational function field $\mathbb{F}_q(T)$ when $q{\equiv}3$ mod 4.

• 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 Chungcheong Mathematical Society
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• v.25 no.2
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• pp.283-289
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• 2012

In this paper, we define the Ono invariants of imaginary quadratic function fields and obtained several results concerning the relations between the Ono invariants and the class numbers.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.183-203
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• 2014

We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.