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27 April 2024

» arxiv » 0910.3715

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Transcendence Measures for some $U_m$-numbers related to Liouville's constant
Ana Paula Chaves ; Diego Marques ;
Date:	20 Oct 2009
Abstract:	In this note, we shall prove that the sum and the product of an algebraic number $alpha$ by the extit{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 $n=1,...,m-1$.
Source:	arXiv, 0910.3715
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