• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.181-185
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• 2009

The Drinfeld modular function ${\mu}$ is a generator of the function field of the Drinfeld modular curve $X_0(T)$ and has an t-expansion with the integral coefficients at infinity. In this paper, we show that the coefficients of ${\mu}$ has congruence properties modulo powers of T.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.529-531
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• 2011

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.375-386
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• 2007

Let p be a prime and $f(z)=\Sigma_{n}a(n)q^n$ be a weakly holomorphic modular function for ${\Gamma}^*_0(p)$ with a(0) = 0. We use Bruinier and Funke's work to find the generating series of modular traces of f(z) as Jacobi forms.

• The Pure and Applied Mathematics
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• v.27 no.2
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• pp.97-108
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• 2020

In this paper, we prove common fixed point theorems for two mappings by using simulation function on fuzzy metric spaces. We also deduce some consequences in modular metric spaces.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.225-238
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• 2014

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.183-188
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• 2008

We will derive recursion formulas satisfied by the traces of singular moduli for the higher level modular function.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2155-2163
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• 2017

Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2012.11a
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• pp.239-241
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• 2012

The major industrialized nations have continued to develop industrialized construction techniques based on automated production processes in factories, and are applying them to a wide range of building. However, the unit modular construction system has had a shorter history of development and application in Korea compared to advanced countries, and consequently, Korean modular builders have a relatively poor technical capacity. So this study is draw a conclusion on the target of priority improvement for idea creation. It study on the enhancement of the functionality of the tool for assemble of Unit Modular that choose the enhancement of the functionality through the analysis of function on the three-level of functional definition and classification, functional arrangement, functional appraisal.

• East Asian mathematical journal
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• v.31 no.5
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• pp.659-665
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• 2015

Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.