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Mathematics of Computation

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


Authors: Chang Heon Kim and Ja Kyung Koo
Journal: Math. Comp. 79 (2010), 1047-1066
MSC (2000): Primary 11F03, 11F06, 11F11, 14H55
DOI: https://doi.org/10.1090/S0025-5718-09-02303-5
Published electronically: September 11, 2009
MathSciNet review: 2600555
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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: https://doi.org/10.1090/S0025-5718-09-02303-5
Received by editor(s): February 16, 2006
Received by editor(s) in revised form: June 15, 2008
Published electronically: September 11, 2009
Additional Notes: The work of the first author was supported by the research fund of Hanyang University (HY-2008-N)
Article copyright: © Copyright 2009 American Mathematical Society

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