On the Zero Attractor of the Euler Polynomials

2004/09/04 by William M. Y. Goh, Goh, William M. Y., Robert Boyer +2 · 1 citation
Mathematics · #05A15 #05C38 #15A15 (Primary) #15A18 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.CO #math.CV #msc:05A15 #msc:05C38 #msc:15A15 #msc:15A18

paper · pdf · doi:10.48550/arxiv.math/0409062

34 pages, 6 figures

arxiv created 2004/09/04 · openalex publication_date 2004/09/04 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szego curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

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