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NORMAL BASES FOR MODULAR FUNCTION FIELDS

Part of: Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  02 March 2017

JA KYUNG KOO ,
DONG HWA SHIN  and
DONG SUNG YOON
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
*
✉math_dsyoon@kaist.ac.kr
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Abstract

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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.

Keywords

modular functionsmodular unitsnormal bases

MSC classification

Primary: 11F03: Modular and automorphic functions
Secondary: 11G16: Elliptic and modular units
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 384 - 392
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

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

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