On Hermite–Padé approximants for the product of logarithms

The talk is devoted to the Hermite–Padé approximants for the systems of functions containing $\ln(1+1/z)\ln(1-1/z)$. We consider two constructions for which an explicit form of approximations can be found. We study their asymptotics and convergence. We discuss number-theoretic applications related to Diophantine approximations of products of logarithms.