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NORMAL BASES FOR MODULAR FUNCTION FIELDS
Part of
- Discontinuous groups and automorphic forms
- Arithmetic algebraic geometry
JA KYUNG KOO, DONG HWA SHIN, DONG SUNG YOON
Journal:

Bulletin of the Australian Mathematical Society / Volume 95 / Issue 3 / June 2017

Published online by Cambridge University Press:

02 March 2017, pp. 384-392

Print publication:

June 2017
- Article
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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.