Diego Marques

collaborators

4 papers

math.NT2026

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,…

math.NT2026

Algebraic values of transcendental power series with geometric coefficient moduli

Diego Marques

Let $λ > 1$ be a real algebraic number. We construct continuum many power series $f (z) = \sum_{k \geq 0} a_{k} z^{k}$ of radius of convergence exactly one such that every nonzero coefficient $…

math.NT2026

Arithmetical structure of sumset intersections

Diego Marques, Melvyn B. Nathanson

The $h$ -fold sumset of a set $A$ of integers is the set of all sums of $h$ not necessarily distinct elements of $A$ . Let $(A_{q})_{q = 1}^{\infty}$ be a strictly decreasing sequence of…

math.NT2025

Some results on asymptotic versions of Mahler's problems

Ricardo Francisco, Diego Marques

In this paper, we show the existence of a transcendental function $f \in Z {z}$ with coefficients that are almost all bounded such that $f$ and all its derivatives assume a…