We improve and extend the irrationality results proved by the authors (Ann. Sc. Norm. Super. PisaCl. Sci.4:3
(2005), 389–437) for dilogarithms of positive rational numbers to results of linear independence
over
of
,
and
for
suitable
,
both for
and for
.
Keywords
polylogarithms, linear independence measures, permutation
group method, saddle-point method in $\mathbb{C}^2$