Vol. 8, No. 1, 2019

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Linear independence of 1, $\mathrm{Li}_1$ and $\mathrm{Li}_2$

Georges Rhin and Carlo Viola

Vol. 8 (2019), No. 1, 81–96
DOI: 10.2140/moscow.2019.8.81
Abstract

We improve and extend the irrationality results proved by the authors (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4:3 (2005), 389–437) for dilogarithms of positive rational numbers to results of linear independence over of 1, Li1(x) and Li2(x) for suitable x , both for x > 0 and for x < 0.

Keywords
polylogarithms, linear independence measures, permutation group method, saddle-point method in $\mathbb{C}^2$
Mathematical Subject Classification 2010
Primary: 11J72
Secondary: 11J82, 33B30
Milestones
Received: 10 January 2018
Accepted: 14 March 2018
Published: 11 August 2018
Authors
Georges Rhin
IECL
Université de Lorraine
UFR MIM
Metz
France
Carlo Viola
Dipartimento di Matematica
Università di Pisa
Pisa
Italy