Irrationality measures of Carlitz zeta values in characteristic \(p\)
type: Item
instance of: scholarly article
title: Irrationality measures of Carlitz zeta values in characteristic \(p\)
zbMATH Open document ID: 0780.11031
author: H. Cherif
author: Bernard de Mathan
published in: Journal of Number Theory
publication date: 1993-10-18T00:00:00Z
review text: Let \(\mathbf{A}= \mathbb{F}_ q[T]\) and put \(\mathbf{K}= \mathbb{F}_ q((q/T))\). Thus \textbf{A} is discrete and compact in \textbf{K}. Let \(i\) be a positive integer. One puts \(\zeta_{\mathbf{A}}(i)= \sum_{n\text{ monic in \textbf{A}}}n^{-i}\). One knows that these sums converge in \textbf{K} to elements which are transcendental over \(\mathbf{k}=\mathbb{F}_ q(T)\). In the paper being reviewed, exact measures of irrationality are calculated for certain of these zeta values.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11J82
Mathematics Subject Classification ID: 11T55
zbMATH DE Number: 431327
zbMATH Keywords: Carlitz zeta values
zbMATH Keywords: exact measures of irrationality
reviewed by: David Goss
MaRDI profile type: Publication
full work available at URL: jnth.1993.1052
OpenAlex ID: W2049761841
DOI: 10.1006/JNTH.1993.1052
description: scientific article; zbMATH DE number 431327