Divisorklassen der Ordnung \(\ell\) bei Kongruenzfunktionenkörpern
type: Item
instance of: scholarly article
title: Divisorklassen der Ordnung \(\ell\) bei Kongruenzfunktionenkörpern
zbMATH Open document ID: 0539.12011
DOI: 10.1007/BF01193913
author: Hans-Georg Rück
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let F be a function field of one variable over a finite field k. For a prime number \(\ell\) denote by \(C(F\cdot \bar k)(\ell)\) the group of divisor classes of order \(\ell\) which are defined over the algebraic closure \(\bar k\) of k. We give an upper bound B for the least number m such that \(C(F\cdot \bar k)(\ell)=C(F\cdot k_ m)(\ell)\) where \((k_ m:k)=m.\) B can be computed with the help of the zeta-function of F. [See also \textit{J. G. D'Mello} and \textit{M. L. Madan}, Manuscr. Math. 41, 75-107 (1983; Zbl 0516.12012)].
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 3857245
zbMATH Keywords: function field of one variable over a finite field
zbMATH Keywords: group of divisor classes
zbMATH Keywords: upper bound
zbMATH Keywords: zeta-function
MaRDI profile type: Publication
cites work: Class group rank relations in \(Z_p\)-extensions
cites work: Q5531596
cites work: On the structure of the class group of a function field
cites work: Die Hasse-Witt-Invariante eines Kongruenzfunktionenkörpers
description: scientific article; zbMATH DE number 3857245