Angular Distribution of Zeros of the Partial Sums of ez via the Solution of Inverse Logarithmic Potential Problem

Abstract

We continue the work of Szegő [18] on describing the angular distribution of the zeros of the normalized partial sum sn(nz) of ez, where \(s _{n}(z):={\sum _{k=0} ^{n}}z ^k/k!\). We imbed this problem in some inverse problem of potential theory and prove a so-called Erdős-Turan-type theorem, which is of interest in itself.