On the closure of the real parts of the zeros of a class of exponential polynomials

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Title: On the closure of the real parts of the zeros of a class of exponential polynomials
Authors: Mora, Gaspar
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Zeros of the partial sums of the Riemann zeta function | Exponential polynomials | Diophantine approximation
Knowledge Area: Análisis Matemático
Issue Date: Apr-2019
Publisher: Springer International Publishing
Citation: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2019, 113(2): 327-332. doi:10.1007/s13398-017-0470-z
Abstract: In this paper we give a characterization of the set RPN(z):={Rz:PN(z)=0}, in terms of the position of a line with respect to an analytic variety, with PN(z) belonging to a large class P(z) of exponential polynomials which can be expressed of the form 1+∑Nj=1aje−zγj.r, where N, M are positive integers, aj∈R with aj≠0, γj=(γj1,γj2,…,γjM), j=1,…,N, are non- null vectors, distinct, with non-negative integers components, r=(r1,r2,…,rM) is a vector of RM with positive rationally independent components, γj.r is the inner product of γj by r in RM, and, for some 1≤jN≤N, is γjN.γj=0 , for all j≠jN.
Sponsor: This work was partially supported by a grant from El Ministerio de Economía y Competitividad, Spain (MTM 2014-52865-P).
URI: http://hdl.handle.net/10045/91593
ISSN: 1578-7303 (Print) | 1579-1505 (Online)
DOI: 10.1007/s13398-017-0470-z
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer-Verlag Italia S.r.l., part of Springer Nature 2017
Peer Review: si
Publisher version: https://doi.org/10.1007/s13398-017-0470-z
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