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arXiv · 0910.3715

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

Ana Paula Chaves·Diego Marques
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Abstract

In this note, we shall prove that the sum and the product of an algebraic number $α$ by the \textit{Liouville constant} $L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degree of $α$ (with respect to $\mathbb{Q}$). Moreover, we shall have that $\max\{w^{\ast}_n(αL),w^{\ast}_n(α+ L)\}\leq 2m^2n+m-1$, for $n=1,...,m-1$.

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BibTeXRIS

Ana Paula Chaves, Diego Marques. 2009-10-19. Transcendence Measures for some $U_m$-numbers related to Liouville's constant. https://arxiv.org/abs/0910.3715

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