• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.379-384
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• 2015

In this paper, we find all Weierstrass points on the hyperelliptic modular curves $X_1(N)$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.541-545
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• 2013

In this paper, we explain how to get defining equations of the modular curves $X_1(2,2N)$ which show the moduli problems and present defining equations of $X_1(2,2N)$ for $N=2,3,{\ldots},8$.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.239-246
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• 2005

We determine the genera of the Drinfeld modular curves $X_\Delta(n)$.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.343-348
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• 2008

In this work, we determine all the modular curves $X_1$(M, N) which are tetragonal.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.443-449
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• 2015

In this paper we propose a method of computing the number of points on the reduction of non-hyperelliptic modular curves of genus greater than or equal to 3 over finite fields.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.305-309
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• 2013

In this paper, we give a new method to get defining equations of modular curves $X_1(2N)$ which show the moduli problems.

• 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 ${\Phi}_N(X, Y )$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.47-59
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• 2007

We find the uniformizers of modular curves $X_{1}(N)\;(N=2,3)$ and explore the relationship with Thompson series and number theoretic property.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.267-270
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• 2010

In this work, we determine all the curves $X^+_1(N)$ which are sub-hyperelliptic.