Linear Forms in Polylogarithms

Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima

Let $r,m$ be positive integers. Let $x$ be a rational number with $0\le x<1$. Consider ${\Phi }_s(x,z)=\sum _{k=0}^{\infty }\frac{z^{k+1}}{{(k+x+1)}^s}$ the $s$-th Lerch…