A note on divisor class groups of degree zero of algebraic function fields over finite fields
type: Item
instance of: scholarly article
title: A note on divisor class groups of degree zero of algebraic function fields over finite fields
zbMATH Open document ID: 1026.11087
DOI: 10.1016/S1071-5797(02)00004-7
author: Ferruh Özbudak
published in: Finite Fields and their Applications
publication date: 2003-04-02T00:00:00Z
review text: Let \(F\) be an algebraic function field over \({\mathbb F}_q\) and let \(P_\infty\) be a degree one place of \(F\). The author considers the group of classes of degree 0 divisors of the form \(P-P_\infty\), where \(P\) runs through the degree one places of \(F\). Let \(E\) denote the exponent of this finite Abelian group. In this note, the author obtains bounds on the number of degree one places of \(F\) in terms of \(E\) and in terms of the maximum number of degree one places of a function field of genus \((E-2)(E-1)/2\).
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 13C20
zbMATH DE Number: 1891479
zbMATH Keywords: algebraic function field
zbMATH Keywords: degree one place
zbMATH Keywords: divisor class group
reviewed by: Robert F. Lax
MaRDI profile type: Publication
cites work: Rational points on curves over finite fields. Theory and Applications
cites work: A Note on Elliptic Curves Over Finite Fields
cites work: Zur Divisorklassengruppe eines Kongruenzfunktionenkörpers
cites work: Algebraic function fields and codes
cites work: Q3997777
full work available at URL: s1071-5797(02)00004-7
OpenAlex ID: W1998842820
description: scientific article; zbMATH DE number 1891479