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The projections of the zeros of exponential polynomials with complex frequencies

Volume 158 / 2019

A. Mas, J. M. Sepulcre Colloquium Mathematicum 158 (2019), 91-102 MSC: Primary 30C15, 30D20; Secondary 30Axx, 52A10. DOI: 10.4064/cm7412-5-2018 Published online: 23 July 2019


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.


  • A. MasDepartamento de Matemáticas
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
  • J. M. SepulcreDepartamento de Matemáticas
    Universidad de Alicante
    03080 Alicante, Spain

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