The projections of the zeros of exponential polynomials with complex frequencies
Volume 158 / 2019
Colloquium Mathematicum 158 (2019), 91-102
MSC: Primary 30C15, 30D20; Secondary 30Axx, 52A10.
DOI: 10.4064/cm7412-5-2018
Published online: 23 July 2019
Abstract
We study the global distribution of zeros of exponential polynomials with complex coefficients and frequencies. For any $P(z)$ in some class of such polynomials, we show that the closure of the projection of $P^{-1}(0)$ on a certain line is a finite union of disjoint segments. We describe this set, in particular we discuss the case where it consists of one segment.
