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arXiv · 1608.06708

Normal bases for modular function fields

Ja Kyung Koo·Dong Hwa Shin·Dong Sung Yoon
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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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Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon. 2016-08-24. Normal bases for modular function fields. https://arxiv.org/abs/1608.06708

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