Diego Marques

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math.NT2026

Values of algebraic functions at Liouville numbers

Yuri Bilu, Diego Marques

In 1953 LeVeque proved the existence of $U_{m}$ -numbers by showing that for some specially defined Liouville number $λ$ , the $m$ th root $λ^{1/ m}$ is in $U_{m}$ . In this article we stud…

math.NT2025

Perfect Sets of Liouville Numbers with Controlled Self-Powers

Sidney A. Morris, Marcelo O. Ribeiro, Diego Marques

We study the arithmetic behavior of self-powers $x^{x}$ when $x$ is a Liouville number. Using recent ideas on strengthened Liouville approximation, we develop flexible constructions…

math.NT2025

Values of generalized Liouville power series at algebraic numbers

Yu. Bilu, D. Marques, C. G. Moreira

For every positive integer $m$ LeVeque (1953) defined the $U_{m}$ -numbers as the transcendental numbers that admit very good approximation by algebraic numbers of degree $m$ , but not…