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

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

2009-10-19

arxiv.org/abs/0910.3715v1

Mathematics

Number Theory

5 pages, no figures

Scientific paper

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 equals to the degree of $\alpha$ (with respect to $\mathbb{Q}$). Moreover, we shall have that $\max\{w^{\ast}_n(\alpha L),w^{\ast}_n(\alpha + L)\}\leq 2m^2n+m-1$, for $n=1,...,m-1$.

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