Untersuchungen zur Theorie der Folgen analytischer Funktionen

  title={Untersuchungen zur Theorie der Folgen analytischer Funktionen},
  author={Robert Jentzsch},
  journal={Acta Mathematica},

The Jentzsch-Szegő Theorem and Balayage Measures

The numerous generalizations of the Jentzsch-Szegő theorem on the location of zeros of Taylor polynomials have been based so far on the extremal properties satisfied by the corresponding

On a generalization of Jentzsch's theorem

The Polynomials of Mahler and Roots of Unity

It is shown that the derivatives of the polynomials of Mahler have all their zeros inside the unit circle.

Zeros of Sections of Power Series: Deterministic and Random

We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erdős and H. Fried) of the so-called Szegő power series. This

Distribution of algebraic numbers

Abstract Schur studied limits of the arithmetic means An of zeros for polynomials of degree n with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are

Hausdorff-Summability of Power Series - the Distribution of Zeros of Hausdorff-Transforms

It is supposed that the order of Η (χ) is ρ = 1, i.e. we have ρ := inf{x(r) = 1 for / < τ < 1} = 1. In this paper we investigate the distribution of the zeros of the polynomials σ„. For an R, > 0 we

A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series

  • F. Bornemann
  • Mathematics
    Computational Methods and Function Theory
  • 2022
Comparing phase plots of truncated series solutions of Kepler’s equation by Lagrange’s power series with those by Bessel’s Kapteyn series strongly suggests that a Jentzsch-type theorem holds true not

Non-normality, topological transitivity and expanding families

  • T. MeyrathJ. Müller
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2021
Abstract We investigate the behaviour of families of meromorphic functions in the neighbourhood of points of non-normality and prove certain covering properties that complement Montel’s Theorem. In