Christian Henriksen

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math.CV2025

Roots of polynomial sequences in root-sparse regions

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Given a family $(q_{k})_{k}$ of polynomials, we call an open set $U$ root-sparse if the number of zeros of $q_{k}$ is locally uniformly bounded on $U$ . We study the interplay between the…

math.CV2024

Value Distributions of Derivatives of $K$ -regular Polynomial Families

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Let $I^c ◯ \in C$ be a domain such that $K := C ∖ I^c ◯$ is compact and non-polar. Let $g_{I^} c ◯$ be the Green's function with a logarithmic pole at infinity, and let…

math.CV2024

Zero distributions of derivatives of polynomial families centering on a set

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Suppose $C \subset C$ is compact. Let $q_{k}$ be a sequence of polynomials of degree $n_{k} \to \infty$ , such that the locus of roots of all the polynomials is bounded, and th…

Roots of polynomial sequences in root-sparse regions

Value Distributions of Derivatives of K-regular Polynomial Families

Zero distributions of derivatives of polynomial families centering on a set

Value Distributions of Derivatives of $K$ -regular Polynomial Families