11 papers
Eremenko's conjecture on higher-order Briot--Bouquet equations
Diego Marques
The Briot--Bouquet theorem describes the meromorphic solutions of autonomous first-order algebraic differential equations. We prove Eremenko's conjecture extending it to all orders…
On Mahler -numbers under rational maps
Diego Marques
In 1906, Maillet proved that every nonconstant rational function over maps Liouville numbers to Liouville numbers. Let be a nonconstant rational function with real…
Arithmetic Rigidity of Analytic Functions and Mahler's Problem on Liouville Numbers
Diego Marques
Let denote the set of Liouville numbers. We prove a local arithmetic rigidity theorem for real-analytic functions. If is an open interval and $f:U\…
Smooth Diffeomorphisms and Mahler's Problem on Liouville Numbers
Diego Marques
A classical theorem of Maillet asserts that every nonconstant rational function over maps Liouville numbers to Liouville numbers. In 1984, Mahler asked whether a trans…
A Neighboring-Denominator Variant of the Erdős--Mahler Conjecture
Diego Marques
We prove a quantitative neighboring-denominator variant of the Erdős-Mahler conjecture. Let be the convergents of an irrational real number . If is …
Height Rigidity for Entire Functions
Diego Marques
We prove that algebraic values of bounded degree and polynomially bounded height are sparse on rational translates of the graph of a transcendental entire function. More precisely,…
Algebraic values of transcendental power series with geometric coefficient moduli
Diego Marques
Let be a real algebraic number. We construct continuum many power series of radius of convergence exactly one such that every nonzero coefficient $…
Arithmetical structure of sumset intersections
Diego Marques, Melvyn B. Nathanson
The -fold sumset of a set of integers is the set of all sums of not necessarily distinct elements of . Let be a strictly decreasing sequence of…
Some results on asymptotic versions of Mahler's problems
Ricardo Francisco, Diego Marques
In this paper, we show the existence of a transcendental function with coefficients that are almost all bounded such that and all its derivatives assume a…
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.
Algebraic periodic points of transcendental entire functions
David Krumm, Diego Marques, Carlos Gustavo Moreira +1
We prove the existence of transcendental entire functions having a property studied by Mahler, namely that and $f^{-1}…