• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.75-81
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• 2023

If a multiplicative function f is commutable with a quadratic form x² + xy + y², i.e., f(x² + xy + y²) = f(x)² + f(x) f(y) + f(y)², then f is the identity function. In other hand, if f is commutable with a quadratic form x² - xy + y², then f is one of three kinds of functions: the identity function, the constant function, and an indicator function for ℕ ＼ pℕ with a prime p.

• 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.

• 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 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.

• 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.

• 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.

• 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.23 no.3
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• pp.547-553
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• 2010

In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.