3 papers
math.NT2026
Values of algebraic functions at Liouville numbers
Yuri Bilu, Diego Marques
In 1953 LeVeque proved the existence of -numbers by showing that for some specially defined Liouville number , the th root is in . In this article we st…
math.NT2026
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 when 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 LeVeque (1953) defined the -numbers as the transcendental numbers that admit very good approximation by algebraic numbers of degree , but not…