# Linear independence of dilogarithmic values

@article{Viola2018LinearIO,
title={Linear independence of dilogarithmic values},
journal={Crelle's Journal},
year={2018},
volume={2018},
pages={193-223}
}
• Published 2018
• Mathematics
• Crelle's Journal
4 Citations
Linear Forms in Polylogarithms
• Mathematics
• ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• 2021
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
We propose a linear independence criterion, and outline an application of it. Down to its simplest case, it aims at solving this problem: given three real numbers, typically as special values ofExpand
Can polylogarithms at algebraic points be linearly independent?
• Mathematics
• 2019
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