• Honam Mathematical Journal
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• v.34 no.4
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• pp.597-601
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• 2012

In this paper we study the density of imaginary cubic function fields having the infinite Hilbert 3-class field tower.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.37-43
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• 1997

Some formulas of the genus numbers and the ambiguous ideal class numbers of function fields are given and these numbers are shown to be the same when the extension is cyclic.

• 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.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.477-483
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• 2012

In this paper we study the infiniteness of the Hilbert ${\ell}$-class field tower of imaginary ${\ell}$-cyclic function fields when ${\ell}{\geq}5$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.161-166
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• 2013

In this paper we study the infiniteness of the Hilbert 3-class field tower of imaginary cubic function fields.

• 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.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.269-274
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• 2011

We investigate the divisor class group of surfaces over finite fields. For some surfaces the divisor class group depends on the characteristic of the field. We calculate the determinant of a matrix which will provide an information about the divisor class group of the surfaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).