Zero distribution of incomplete Padé and Hermite–Padé approximations

Abstract

We prove that a subsequence of the normalized zero counting measures of incomplete Padé approximants tend, as the degree of the numerators goes to infinity and that of the denominators remains bounded, to the uniform distribution on the largest circle centered at the origin inside of which the approximants converge in the sense of the Hausdorff content. As a consequence, a Jentzsch-Szegő type theorem for row sequences of Hermite-Padé approximants is given.

On Row Sequences of Hermite–Padé Approximation and Its Generalizations

“…, d, in Equation 7is irrelevant to our interest in this paper. However, it is worth mentioning the paper [45] where la Calle Ysern and Mínguez Ceniceros studied the distribution of zeros of P n,m, , = 1, 2, . .…”