arXiv subjects

M. Bello-Hernández

Publications and source records attributed to M. Bello-Hernández.

3 recordsLinked to original sources

arXiv2026

A Divisor Parametrization for the Erdős--Straus Conjecture

We study representations of $1/n$ as a sum of three unit fractions whose denominators are all divisible by a prescribed integer $m$. After scaling, this is equivalent to representing $m/n$ as a sum of three unit fractions. Our main focus is the Erdős--Straus case $m=4$. We introduce a divisor-based function $\mathrm{fab}(n,a,b)$, prove that its admissible parameters recover exactly the decompositions of $1/n$ with all three denominators divisible by $4$, and compare this parametrization with well-known Type I/II descriptions.

math.NT↗

arXiv2026

Asymptotics and zero behaviour of geometric polynomials

We obtain some results on the asymptotic behaviour of Geometric polynomials in both the complex plane minus $[-1,0]$ and the interval $(-1,0)$. We also find the distance of consecutive zeros of these polynomials in the bulk of the interval $(-1,0)$. We also prove that they satisfy certain orthogonality properties. Due to their relationship with Eulerian polynomials, the results for Geometric polynomials can be transferred to Eulerian polynomials verbatim.

math.CA↗

arXiv2005

Fourier-Padé approximants for Angelesco systems

In this paper we study linear and non-linear Fourier-Padé approximation for Angelesco systems of functions. This construction is similar to that of Hermite-Padé approximation. Instead of considering power series expansions of the functions in the system, we take their expansion in a series of orthogonal polynomials.

math.CA↗