KUCERA GROUP OF CIRCULAR UNITS IN FUNCTION FIELDS

Title & Authors
KUCERA GROUP OF CIRCULAR UNITS IN FUNCTION FIELDS
Ahn, Jae-Hyun; Jung, Hwan-Yup;

Abstract
Let $\small{\mathbb{A}=\mathbb{F}_q}$[T] be the polynomial ring over a finite field $\small{\mathbb{F}_q}$[T] and K=$\small{\mathbb{F}_q}$(T) its field of fractions. Let $\small{{\ell}}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $\small{P{\in}{\mathbb{A}}}$ with deg $\small{P{\equiv}0}$ (mod $\small{{\ell})}$. In this paper we define the group $\small{C_K}$ of circular units in K=k$\small{(\{\sqrt[{\ell}]P\;:\;P{\in}J\})}$ in the sense of Kucera [4] and compute the index of $\small{C_K}$ in the full unit group $\small{O^*_K}$.
Keywords
Kucera group;circular units;function fields;
Language
English
Cited by
1.
ON THE PARITY OF THE CLASS NUMBER OF SOME REAL BIQUADRATIC FUNCTION FIELD,;;

충청수학회지, 2010. vol.23. 1, pp.169-176
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