Transcendence and the Carlitz-Goss gamma function
type: Item
instance of: scholarly article
title: Transcendence and the Carlitz-Goss gamma function
zbMATH Open document ID: 0874.11042
author: Michel Mendès France
author: Jia-Yan Yao
published in: Journal of Number Theory
publication date: 1997-05-19T00:00:00Z
review text: Let \({\mathcal A}:=\mathbb{F}_q[T]\), \(k:=\mathbb{F}_q(T)\) and \({\mathcal K}:=\mathbb{F}_q((1/T))\). It is possible to define a ``factorial'' for \(\mathcal A\). This factorial has many of the properties of the classical \(n!\). Moreover, by taking its ``one-unit part'', this factorial interpolates to a continuous gamma function from \(\mathbb{Z}_p\) to \({\mathcal K}^*\). In the beautiful paper being reviewed, the authors establish that the values of this gamma function at all arguments NOT in \(\mathbb{N}= \{0,1,2,\dots\}\) are transcendental over \(k\). This finishes a line of research begun by D. Thakur and pursued by A. Thiery, J. Yu, L. Denis and J.-P. Allouche.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11J81
zbMATH DE Number: 1011062
zbMATH Keywords: Carlitz function
zbMATH Keywords: transcendental values
zbMATH Keywords: continuous gamma function
reviewed by: David Goss
MaRDI profile type: Publication
full work available at URL: jnth.1997.2104
OpenAlex ID: W2035221903
cites work: Sur la transcendance de la série formelle Π
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DOI: 10.1006/JNTH.1997.2104
description: scientific article; zbMATH DE number 1011062