University of Oulu

Bundschuh, P., Väänänen, K. (2018) Hypertranscendence and algebraic independence of certain infinite products. Acta Arithmetica, 184 (1), 51-66. doi:10.4064/aa170528-16-12

Hypertranscendence and algebraic independence of certain infinite products

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Author: Bundschuh, Peter1; Väänänen , Keijo2
Organizations: 1Mathematisches Institut, Universität zu Köln, Weyerta, 86-90, 50931 Köln, Germany
2Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Polish Academy of Sciences, Institute of Mathematics, 2018
Publish Date: 2019-03-28


We study infinite products \(F(z)=\prod_{j\ge0}p(z^{d^j})\), where \(d\ge2\) is an integer and \(p\in\mathbb{C}[z]\) with \(p(0)=1\) has at least one zero not lying on the unit circle. In that case, \(F\) is a transcendental function and we are mainly interested in conditions for its hypertranscendence. Moreover, we investigate finite sets of infinite products of type \(F\) and show that, under certain natural assumptios, these functions and their first derivatives are algebraically independent over \(\mathbb{C}(z)\).

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Series: Acta arithmetica
ISSN: 0065-1036
ISSN-E: 1730-6264
ISSN-L: 0065-1036
Volume: 184
Issue: 1
Pages: 51 - 66
DOI: 10.4064/aa170528-16-12
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © Instytut Matematyczny PAN, 2018.