Linear independence of dilogarithmic values

@article{Viola2018LinearIO,
  title={Linear independence of dilogarithmic values},
  author={Carlo Viola and Wadim Zudilin},
  journal={Crelle's Journal},
  year={2018},
  volume={2018},
  pages={193-223}
}
Linear Forms in Polylogarithms
Let $r, \,m$ be positive integers. Let $x$ be a rational number with $0 \le x <1$. Consider $\Phi_s(x,z) =\displaystyle\sum_{k=0}^{\infty}\frac{z^{k+1}}{{(k+x+1)}^s}$ the $s$-th Lerch function withExpand
Vectors of type II Hermite–Padé approximations and a new linear independence criterion
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Can polylogarithms at algebraic points be linearly independent?
Let $r,m$ be positive integers. Let $0\le x <1$ be a rational number. Let $\Phi_s(x,z)$ be the $s$-th Lerch function $\sum_{k=0}^{\infty}\tfrac{z^{k+1}}{(k+x+1)^s}$ with $s=1,2,\ldots ,r$. WhenExpand

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