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NORMAL BASES FOR MODULAR FUNCTION FIELDS

Published online by Cambridge University Press:  02 March 2017

JA KYUNG KOO
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea email jkkoo@math.kaist.ac.kr
DONG HWA SHIN
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 17035, Republic of Korea email dhshin@hufs.ac.kr
DONG SUNG YOON
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea email math_dsyoon@kaist.ac.kr

Abstract

We provide a concrete example of a normal basis for a finite Galois extension which is not abelian. More precisely, let $\mathbb{C}(X(N))$ be the field of meromorphic functions on the modular curve $X(N)$ of level $N$ . We construct a completely free element in the extension $\mathbb{C}(X(N))/\mathbb{C}(X(1))$ by means of Siegel functions.

Type
Research Article
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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Footnotes

The second author was supported by Hankuk University of Foreign Studies Research Fund of 2016.

References

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