On the existence of equivalent Dirichlet polynomials whose zeros preserve a topological property

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Title: On the existence of equivalent Dirichlet polynomials whose zeros preserve a topological property
Authors: Dubon, Eric | Sepulcre, Juan Matias
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Dirichlet polynomials | Dirichlet character | Multiplicative functions | Bohr’s equivalence | Zeros of entire functions
Knowledge Area: Análisis Matemático
Issue Date: Apr-2018
Publisher: World Scientific Publishing
Citation: International Journal of Number Theory. 2018, 14: 713. doi:10.1142/S1793042118500458
Abstract: In this paper, we study the distribution of zeros of the ordinary Dirichlet polynomials which are generated by an equivalence relation introduced by Harald Bohr. Through the use of completely multiplicative functions, we construct equivalent Dirichlet polynomials which have the same critical strip, where all their zeros are situated, and satisfy the same topological property consisting of possessing zeros arbitrarily near every vertical line contained in some substrips inside their critical strip. We also show that the real projections of the zeros of the partial sums of the alternating zeta function, for some particular cases, are dense in their critical intervals.
Sponsor: The second author's research was partially supported by Generalitat Valenciana under project GV/2015/035.
URI: http://hdl.handle.net/10045/74847
ISSN: 1793-0421 (Print) | 1793-7310 (Online)
DOI: 10.1142/S1793042118500458
Language: eng
Type: info:eu-repo/semantics/article
Rights: © World Scientific Publishing
Peer Review: si
Publisher version: https://doi.org/10.1142/S1793042118500458
Appears in Collections:INV - CADAGL - Artículos de Revistas

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