A note on Hadamard roots of rational functions
type: Item
instance of: scholarly article
title: A note on Hadamard roots of rational functions
zbMATH Open document ID: 0958.11009
published in: Rocky Mountain Journal of Mathematics
publication date: 1997-07-27T00:00:00Z
full work available at URL: contents.htm
review text: Let \(F\) be a polynomial such that \(\sum_{k\geq 0} F(b_k) X^k\) is a rational function. Generalizing a conjecture of Pisot, the author considers the following conjecture: Suppose that all the \(b_k\) belong to a fixed field finitely generated over \({\mathbb Q}\), then prove that there exists a rational function \(\sum_{k\geq 0} c_k X^k\) such that \(F(c_k)=F(b_k)\) for all \(k\geq 0\). The paper contains a very detailed discussion of this problem and a comparison with the Hadamard quotient problem (solved by the author in 1988). Many ideas are proposed to try to get a proof of this conjecture.
reviewed by: Maurice Mignotte
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1026410
zbMATH Keywords: Hadamard product
zbMATH Keywords: rational functions
author: Alfred J. van der Poorten
MaRDI profile type: Publication
OpenAlex ID: W2161045065
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DOI: 10.1216/RMJM/1181072044
description: scientific article; zbMATH DE number 1026410