Normal bases for modular function fields

Ja Kyung Koo; Dong Hwa Shin; Dong Sung Yoon

Normal bases for modular function fields

Number Theory 2018-02-02 v1

Authors: Ja Kyung Koo , Dong Hwa Shin , Dong Sung Yoon

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.

Keywords

galois theory

Cite

@article{arxiv.1608.06708,
  title  = {Normal bases for modular function fields},
  author = {Ja Kyung Koo and Dong Hwa Shin and Dong Sung Yoon},
  journal= {arXiv preprint arXiv:1608.06708},
  year   = {2018}
}

Comments

8 pages

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