• 대한수학회논문집
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• 제24권2호
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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.

• 충청수학회지
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• 제24권3호
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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 ${\Phi}_N(X, Y )$.

• 충청수학회지
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• 제20권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권2호
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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.

• 대한수학회지
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• 제52권2호
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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.

• 대한수학회지
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• 제51권2호
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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.

• 충청수학회지
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• 제21권2호
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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.

• 대한수학회보
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• 제54권6호
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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.

• 한국건축시공학회:학술대회논문집
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• 한국건축시공학회 2012년도 추계 학술논문 발표대회
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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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• 제31권5호
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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.