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

2009/10/19 by Ana Paula Chaves, Chaves, Ana Paula, Diego Marques +1
Mathematics · Physics and Astronomy · #11J82 #11K60 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0910.3715

openalex publication_date 2009/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we shall prove that the sum and the product of an algebraic number α by the Liouville constant L=∑_j=1^∞10^-j! is a U-number with type equals to the degree of α (with respect to ℚ). Moreover, we shall have that max\w^∗_n(αL),w^∗_n(α+ L)\≤ 2m²n+m-1, for n=1,...,m-1.

Related

• Values of generalized Liouville power series at algebraic numbers
• Transcendence of some infinite series
• A new transcendence measure for the values of the exponential function at algebraic arguments
• On the transcendence of some operations of infinite series
• Transcendence of Power Series for Some Number Theoretic Functions