A transcendence criterion for infinite products
type: Item
instance of: scholarly article
title: A transcendence criterion for infinite products
zbMATH Open document ID: 1207.11075
DOI: 10.4171/RLM/496
author: Pietro Corvaja
author: Jaroslav Hančl
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2008-06-25T00:00:00Z
review text: The authors prove a transcendence criterion for certain infinite products of algebraic numbers. For an increasing sequence of positive integers \(a_n\) and an algebraic number \(\alpha>1\), they study the convergent infinite product \(\prod_{n}([\alpha^{a_n}]/\alpha^{a_n})\), where \([\cdot]\) denotes the integral part. It is proved in Theorem 1 that its value is transcendental, under certain hypotheses; whereas Theorem 3 shows that such hypotheses are in a sense unavoidable. This is done by applying a result of the first author and \textit{U. Zannier} [Acta Math. 193, No. 2, 175--191 (2004; Zbl 1175.11036)].
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 11J68
zbMATH DE Number: 5292681
zbMATH Keywords: transcendence criterion
zbMATH Keywords: infinite products
MaRDI profile type: Publication
cites work: Q4539513
cites work: On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France
cites work: Diophantine approximations and diophantine equations
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description: scientific article; zbMATH DE number 5292681