• 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.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• Journal of Multimedia Information System
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• v.6 no.4
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• pp.323-328
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• 2019

In this paper, a method of constructing an advanced sequential circuit over finite fields is proposed. The method proposed an algorithm for assigning all elements of finite fields to digital code from the properties of finite fields, discussed the operating characteristics of T-gate used to construct sequential digital system of finite fields, and based on this, formed sequential circuit without trajectory. For this purpose, the state transition diagram was allocated to the state dependency code and a whole table was drawn showing the relationship between the status function and the current state and the previous state. The following status functions were derived from the status function and the preceding table, and the T-gate and the device were used to construct the sequential circuit. It was confirmed that the proposed method was able to organize sequential digital systems effectively and systematically.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.1-9
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• 1997

We obtained some class fields associated to an order R of a function field and evaluated the valuation of the invariant $\xi (c)$ for an invertible ideal c of R.

• International Journal of Ocean System Engineering
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• v.3 no.3
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• pp.131-135
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• 2013

We construct the fundamental fields for 3-D arbitrarily shaped plane cracks in by differentiating with respect to a parameter of the crack. As an application of these fundamental fields, the total elastic energy release rate in combined mode cracking is computed.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• 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 ${\ell}{\geq}5$.