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NORMAL BASES FOR FUNCTION FIELDS

Part of: Algebraic number theory: global fields Discontinuous groups and automorphic forms Field extensions Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 May 2024

YOSHINORI HAMAHATA Open the ORCID record for YOSHINORI HAMAHATA [Opens in a new window]
YOSHINORI HAMAHATA*
Affiliation:
Department of Applied Mathematics Okayama University of Science, Ridai-cho 1-1, Okayama 700-0005, Japan
*
e-mail: hamahata@ous.ac.jp
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Abstract

In function fields in positive characteristic, we provide a concrete example of completely normal elements for a finite Galois extension. More precisely, for a nonabelian extension, we construct completely normal elements for Drinfeld modular function fields using Siegel functions in function fields. For an abelian extension, we construct completely normal elements for cyclotomic function fields.

Keywords

normal basisDrinfeld modular function fieldSiegel functioncyclotomic function field

MSC classification

Primary: 11F52: Modular forms associated to Drinfel'd modules
Secondary: 11G16: Elliptic and modular units 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.) 12F05: Algebraic extensions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 1 , August 2024 , pp. 44 - 55
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by JSPS KAKENHI Grant Number 21K03192.

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