• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.529-572
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• 2012

A basis of a subspace of $S_4({\Gamma}_0(79))$ is given and the formulas for the number of representations of positive integers by some direct sums of the quadratic forms $x^2_1+x_1x_2+20x^2_2$, $4x^2_1{\pm}x_1x_2+5x^2_2$, $2x^2_1{\pm}x_1x_2+10x^2_2$ are determined.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.645-689
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• 2016

This article gives upper bounds on the number of Fourier-Jacobi coefficients that determine a paramodular cusp form in degree two. The level N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.507-530
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• 2018

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.319-330
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• 2023

In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of Lü and Wang in this direction.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.281-285
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• 2018

Let $S_k(N)$ be the space of cusp forms of weight k for ${\Gamma}_0(N)$. We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight k for the group ${\Gamma}_0^+(N)$ generated by ${\Gamma}_0(N)$ and $W_N$ and $S_k^-(N)$ is the subspace consisting of elements f in $S_k(N)$ satisfying $f{\mid}_kW_N=-f$. We find generators spanning the space $S_k^-(N)$ from $Poincar{\acute{e}}$ series and give all linear relations among such generators.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.237-255
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• 2023

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

• Communications of the Korean Mathematical Society
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• v.7 no.1
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• pp.69-80
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• 1992

• The korean journal of orthodontics
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• v.26 no.5 s.58
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• pp.535-546
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• 1996

The purpose of this study was to classify mandibular dental arch forms based on Raberin's method, and to compare Raberin's arch forms with that of the Korean's, and to designate arch form of bracket level according to distance between cusp tip and buccal surface of bracket level. The sample consisted of 159 mandibular dental casts showing normal occlusion which was taken from 62 males and 97 females of the Korean, aging from 13 to 25 years. The model was taken by X-ray. The landmarks were cusp points which expressed the mandibular dental arch line of cusp tips and buccal points which were measured from cusp tips to buccal surfaces of bracket level. The landmarks on the film were digitized, and measurements and statistics were performed. The results were as follows; 1. The models were classified as type 1, type 2, type 3, type 4 and type 5 by the author, and polynomial functions of the six degree and R-square values were calculated using statistical method, and each calculated equations explained each group with the least R-square value of 0.97, and each arch forms' were plotted. 2. The distribution of type 1 was $17.6\%$, type 2 $20.8\%$, type 3 $20.8\%$, type 4 $16.3\%$ and type 5 $24.5\%$. 3. The Korean arch form was characterized by larger width, smaller height compared to the French arch form. 4. The designated arch form of bracket level, viz the distance between cusp point and buccal point was calculated. The distance between cusp point and buccal point of incisor was 1mm, canine 1.9mm, first premolar 2.5mm, second premolar 2.6mm, first molar 2.7mm and second molar 2.7mm.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.509-514
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• 2016

By constructing a canonical basis for the space $M_k^{\sharp}({\Gamma}_0(N))$ explicitly, we find a basis of the space of cusp forms for ${\Gamma}_0(N)$ consisting of $Poincar{\acute{e}}$ series.