• 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.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.19-29
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• 2006

In this paper, we obtain some inequalities similar to Hilbert type. Some new inequalities are also given.

• 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.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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.403-409
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• 2013

In [20] and [22], the author proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t{\leq}10$ and $t{\leq}s$ has generic Hilbert function. In this paper, we prove that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t$ and $({a\atop2})-1{\leq}s$ has also generic Hilbert function.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.563-572
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• 2009

In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.119-125
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• 2015

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.