Dubon, Eric, Sepulcre, Juan Matias
On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials
Experimental Mathematics. 2014, 23(1): 13-24. doi:10.1080/10586458.2013.853630
URI: http://hdl.handle.net/10045/45566
DOI: 10.1080/10586458.2013.853630
ISSN: 1058-6458 (Print)
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.
Keywords:Dirichlet polynomials, Fractal strings, Complex dimensions of fractal strings, Set of dimensions of fractality, Zeros of entire functions
Taylor & Francis
info:eu-repo/semantics/article