• 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.27 no.2
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• pp.223-231
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• 2012

We obtain some density results for the 4-ranks of class groups of quadratic extensions of quadratic function fields analogous to those results of F. Gerth in the classical case.

• 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.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.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.779-796
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• 2024

In this paper, under the ABC-conjecture, we show that there exist infinitely many real quadratic fields with odd period of minimal type.

• 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.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.219-226
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• 2014

In this paper we study the infiniteness of Hilbert 2-class field towers of real quadratic function fields over $\mathbb{F}_q(T)$, where q is a power of an odd prime number.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.1049-1060
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• 2013

In this paper we study the infiniteness of Hilbert 2-class field towers of imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1149-1161
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• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.699-704
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• 2010

In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.