Dubon, Eric, Sepulcre, Juan Matias
On the existence of equivalent Dirichlet polynomials whose zeros preserve a topological property
International Journal of Number Theory. 2018, 14: 713. doi:10.1142/S1793042118500458
URI: http://hdl.handle.net/10045/74847
DOI: 10.1142/S1793042118500458
ISSN: 1793-0421 (Print)
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.
Keywords:Dirichlet polynomials, Dirichlet character, Multiplicative functions, Bohr’s equivalence, Zeros of entire functions
World Scientific Publishing
info:eu-repo/semantics/article