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NORMAL BASES FOR MODULAR FUNCTION FIELDS
Published online by Cambridge University Press: 02 March 2017
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.
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- Research Article
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- 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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