On the non-isolation of the real projections of the zeros of exponential polynomials

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Title: On the non-isolation of the real projections of the zeros of exponential polynomials
Authors: Sepulcre, Juan Matias | Vidal, Tomás
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Zeros of entire functions | Exponential polynomials | Partial sums of the Riemann zeta function | Kronecker theorem
Knowledge Area: Análisis Matemático
Issue Date: 1-May-2016
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2016, 437(1): 513-525. doi:10.1016/j.jmaa.2016.01.014
Abstract: This paper proves that the real projection of each zero of any function P(z)P(z) in a large class of exponential polynomials is an interior point of the closure of the set of the real parts of the zeros of P(z)P(z). In particular it is deduced that, for each integer value of n≥17n≥17, if z0=x0+iy0z0=x0+iy0 is an arbitrary zero of the n th partial sum of the Riemann zeta function ζn(z)=∑j=1n1jz, there exist two positive numbers ε1ε1 and ε2ε2 such that any point in the open interval (x0−ε1,x0+ε2)(x0−ε1,x0+ε2) is an accumulation point of the set defined by the real projections of the zeros of ζn(z)ζn(z).
Sponsor: The first author’s research was partially supported by Generalitat Valenciana under project GV/2015/035.
URI: http://hdl.handle.net/10045/62689
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2016.01.014
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2016 Elsevier Inc.
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2016.01.014
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