Extension of Baker's analogue of Littlewood's diophantine approximation problem
type: Item
instance of: scholarly article
title: Extension of Baker's analogue of Littlewood's diophantine approximation problem
zbMATH Open document ID: 0756.11017
author: Takao Komatsu
published in: Kodai Mathematical Journal
publication date: 1992-09-26T00:00:00Z
review text: Verf. beweist folgenden Satz: Sind \(\lambda_ 1,\dots,\lambda_ r\in\mathbb{R}^ \times\) paarweise verschieden und sind \(u_ 0,\dots,u_ r\in\mathbb{R}[t]\), \(u_ 0\neq 0\), so gilt \[ | u_ 0(t)|\prod_{\rho=1}^ r | u_ \rho(t)-u_ 0(t)\exp(\lambda_ \rho t^{-n})|\geq\exp(-{1\over 2}n(r^ 3+r)), \] wobei einer von Null verschiedenen formalen Laurentreihe \(a_ m t^ m+a_{m-1}t^{m-1}+\dots\in\mathbb{R}\{t^{-1}\}\) mit \(a_ m\neq 0\) unter \(|\dots|\) der Wert \(e^ m\) zugeordnet ist. Im Fall \(n=1\) reduziert sich dies Ergebnis auf eines von \textit{A. Baker} [Mich. Math. J. 11, 247-250 (1964; Zbl 0218.10052)], dessen Beweis nur für \(r=2\) ausgeführt worden war.
reviewed by: Peter Bundschuh
Mathematics Subject Classification ID: 11J61
zbMATH DE Number: 55868
zbMATH Keywords: Littlewood's diophantine approximation problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039458
OpenAlex ID: W2069036660
cites work: An analogue of a problem of Littlewood
cites work: On an analogue of Littlewood's diophantine approximation problem
DOI: 10.2996/KMJ/1138039458
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description: scientific article; zbMATH DE number 55868