Asymptotics of a sequence of Witt vectors
type: Item
instance of: scholarly article
title: Asymptotics of a sequence of Witt vectors
zbMATH Open document ID: 0764.41028
DOI: 10.1016/0021-9045(92)90006-A
author: Shituo Lou
author: Jonathan M. Borwein
published in: Journal of Approximation Theory
publication date: 1993-01-16T00:00:00Z
review text: The paper gives the asymptotics and order estimates of the numbers \(d_ n\) appearing in \[ \prod_{n\geq1}{1\over {1+d_ nt^ n/n!}}=(1-t)e^ t. \] The numbers \(d_ n\) are positive integers. It is shown that, for \(n=2,3,\ldots\), \(d_ n\leq(n-1)!\) when \(n\) is odd, \(d_ n=(n-1)!\), when \(n\) is prime, \(d_ n\geq(n-1)!\), when \(n\) is even, and that \(1-1/n\leq d_ n/(n-1)!\leq1+\alpha_ n/\sqrt{(n)}\), where \(\alpha_ 8=\alpha_{16}=2\), and otherwise \(\alpha_ n=1\). The numbers \(d_ n\) give the dimensions of certain group representations, in which theory also Witt vectors occur.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 13K05
zbMATH DE Number: 89636
zbMATH Keywords: Witt vectors
reviewed by: Nico M. Temme
MaRDI profile type: Publication
cites work: Q5555033
cites work: Witt vectors and the algebra of necklaces
description: scientific article; zbMATH DE number 89636