Some numerical results on the behavior of zeros of the Hermite-Padé polynomials

Abstract: We introduce and analyze some numerical results obtained by the authors experimentally. These experiments are related to the well known problem about the distribution of the zeros of Hermite--Pad\'e polynomials for a collection of three functions $[f_0 \equiv 1,f_1,f_2]$. The numerical results refer to two cases: a pair of functions $f_1,f_2$ forms an Angelesco system and a pair of functions $f_1=f,f_2=f^2$ forms a (generalized) Nikishin system. The authors hope that the obtained numerical results will set up a new conjectures about the limiting distribution of the zeros of Hermite--Pad\'e polynomials.