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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
ℚ
of
1 ,
Li 1 ( x ) and
Li 2 ( x ) for
suitable
x
∈
ℚ ,
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