Transcendence Measures for some $U_m$-numbers related to Liouville's constant

Ana Paula Chaves, Diego Marques

In this note, we shall prove that the sum and the product of an algebraic number $\alpha$ by the \textit{Liouville constant} $L={\sum }_{j=1}^{\infty }10^{-j!}$ is a $U$-number with type eq…