4 papers
Geometric Progressions meet Zeckendorf Representations
Diego Marques, Pavel Trojovsky
Motivated by Erdős' ternary conjecture and by recent work of Cui--Ma--Jiang [``Geometric progressions meet Cantor sets'', \textit{Chaos Solitons Fractals} \textbf{163} (2022), 1125…
Asymptotic error terms in Bonse-type inequalities
Diego Marques, Pavel Trojovsky
Let denote the -th prime. In 2000, Panaitopol established the inequality for all , where is the prime counting funct…
On the Transcendence of Power Towers of Liouville Numbers
Diego Marques, Marcelo Oliveira, Pavel Trojovsk\' y
In this paper, among other things, we explicit a -dense set of Liouville numbers, for which the triple power tower of any of its elements is a transcendental number.
On the Arithmetic Behavior of Liouville Numbers under Rational Maps
Ana Paula Chaves, Diego Marques, Pavel Trojovsk\' y
In 1972, Alniaçik proved that every strong Liouville number is mapped into the set of -numbers, for any non-constant rational function with coefficients belonging to an -de…