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Generators of function fields of the modular curves $ X_1(5)$ and $ X_1(6)$

Author(s): Chang Heon Kim; Ja Kyung Koo.
Journal: Math. Comp.
MSC (2000): Primary 11F03, 11F06, 11F11, 14H55
Posted: September 11, 2009
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Abstract: We show that the modular functions $ j_{1,5}$ and $ j_{1,6}$ generate function fields of the modular curves $ X_1(N)$ ($ N=5,6$, respectively) and find some number-theoretic properties of these modular functions.

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Additional Information:

Chang Heon Kim
Affiliation: Department of Mathematics, Hanyang University, Seoul, 133-791 Korea
Email: chhkim@hanyang.ac.kr

Ja Kyung Koo
Affiliation: Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701 Korea
Email: jkkoo@math.kaist.ac.kr

DOI: 10.1090/S0025-5718-09-02303-5
PII: S 0025-5718(09)02303-5
Received by editor(s): February 16, 2006
Received by editor(s) in revised form: June 15, 2008
Posted: September 11, 2009
Additional Notes: The work of the first author was supported by the research fund of Hanyang University (HY-2008-N)
Copyright of article: Copyright 2009, American Mathematical Society

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