A note on linear independence of polylogarithms over the rationals
type: Item
instance of: scholarly article
title: A note on linear independence of polylogarithms over the rationals
zbMATH Open document ID: 1286.11108
author: Noriko Hirata-Kohno
author: Hironori Okada
published in: Proceedings of the Japan Academy. Series A
publication date: 2013-04-25T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1352210378
review text: The paper contains a new lower bound for the dimension of the linear space over the rationals spanned by \(1\) and values of polylogarithms of a given rational number. As a special case the authors prove the following theorem. Let \(\alpha=\frac{p}{q}\) be a rational number with \(0<|\alpha|<1\) and \(q\leq50\). Let \(s\geq356\). Then \[ \dim_{\mathbb Q}\bigl(\mathbb Q+\mathbb Q\, Li_1(\alpha)+\dots+\mathbb Q\, Li_s(\alpha)\bigr)\geq3 \] where \(Li\) is the polylogarithmic function.
reviewed by: Jan Šustek
Mathematics Subject Classification ID: 11J72
Mathematics Subject Classification ID: 11G55
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 6157755
zbMATH Keywords: polylogarithms
zbMATH Keywords: Padé approximation
zbMATH Keywords: irrationality
zbMATH Keywords: linear independence
MaRDI profile type: Publication
OpenAlex ID: W2007622316
cites work: A refinement of Nesterenko's linear independence criterion with applications to zeta values
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cites work: Q4001952
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cites work: Linear independence of values of polylogarithms
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cites work: Q5508372
DOI: 10.3792/PJAA.88.156
description: scientific article; zbMATH DE number 6157755