Angular Distribution of Zeros of the Partial Sums of ez via the Solution of Inverse Logarithmic Potential Problem

2006 ◽  
Vol 6 (2) ◽  
pp. 447-458 ◽  
Author(s):  
Vladimir V. Andrievskii ◽  
Amos J. Carpenter ◽  
Richard S. Varga
Keyword(s):  
Angular Distribution ◽  
Potential Problem ◽  
Logarithmic Potential ◽  
Partial Sums ◽  
Distribution Of Zeros

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

2018 ◽  
Vol 14 (03) ◽  
pp. 713-725
Author(s):  
Eric Dubon ◽  
Juan Matías Sepulcre
Keyword(s):  
Zeta Function ◽  
Equivalence Relation ◽  
Topological Property ◽  
Vertical Line ◽  
Partial Sums ◽  
Critical Strip ◽  
Multiplicative Functions ◽  
Distribution Of Zeros ◽  
Dirichlet Polynomials ◽  
Alternating Zeta Function

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.

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