Galois groups and genera of a kind of quasi-cyclotomic function fields

Min Sha*, Linsheng Yin

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We call a (q - 1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the structure of the Galois groups of a kind of quasi-cyclotomic function fields over the base field. We also give the genus formulae of them.

Original languageEnglish
Pages (from-to)2574-2581
Number of pages8
JournalJournal of Number Theory
Volume132
Issue number11
DOIs
Publication statusPublished - Nov 2012
Externally publishedYes

Keywords

  • cyclotomic function field
  • galois group
  • genus
  • quasi-cyclotomic function field

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