• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.249-256
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• 2016

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.403-414
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• 2019

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.173-184
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• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.265-294
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• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.

• Journal of The Korean Astronomical Society
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• v.50 no.3
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• pp.61-70
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• 2017

We study the angular correlation function of bright ($K_s{\leq}19.5$) Extremely Red Objects (EROs) selected in the Subaru GTO 2$deg^2$ field. By applying the color selection criteria of $R-K_s$ > 5.0, 5.5, and 6.0, we identify 9055, 4270, and 1777 EROs, respectively. The number density is consistent with similar studies on the optical - NIR color selected red galaxies. The angular correlation functions are derived for EROs with different limiting magnitude and different $R-K_s$ color cut. When we assume that the angular correlation function $w({\theta})$ follows a form of a power-law (i.e., $w({\theta})=A{\theta}^{-{\delta}}$), the value of the amplitude A was larger for brighter EROs compared to the fainter EROs. The result suggests that the brighter, thus more massive high-redshift galaxies, are clustered more strongly compared to the less massive galaxies. Assuming that EROs have redshift distribution centered at ~ 1.1 with ${\sigma}_z=0.15$, the spatial correlation length $r_0$ of the EROs estimated from the observed angular correlation function ranges ${\sim}6-10h^{-1}Mpc$. A comparison with the clustering of dark matter halos in numerical simulation suggests that the EROs are located in most massive dark matter halos and could be progenitors of $L_{\ast}$ elliptical galaxies.