On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

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Title: On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials
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 Análisis Matemático
Keywords: Dirichlet polynomials | Fractal strings | Complex dimensions of fractal strings | Set of dimensions of fractality | Zeros of entire functions
Knowledge Area: Análisis Matemático
Issue Date: 12-Mar-2014
Publisher: Taylor & Francis
Citation: Experimental Mathematics. 2014, 23(1): 13-24. doi:10.1080/10586458.2013.853630
Abstract: In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.
Sponsor: The second author was partially supported by Vicerrectorado de Investigación, Desarrollo e Innovación de la Universidad de Alicante under project GRE11-23.
URI: http://hdl.handle.net/10045/45566
ISSN: 1058-6458 (Print) | 1944-950X (Online)
DOI: 10.1080/10586458.2013.853630
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Taylor & Francis Group, LLC
Peer Review: si
Publisher version: http://dx.doi.org/10.1080/10586458.2013.853630
Appears in Collections:INV - CADAGL - Artículos de Revistas

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