alternating zeta function
Recently Published Documents


TOTAL DOCUMENTS

5
(FIVE YEARS 1)

H-INDEX

1
(FIVE YEARS 0)

Author(s):  
Takashi Komatsu ◽  
Norio Konno ◽  
Iwao Sato

2018 ◽  
Vol 14 (03) ◽  
pp. 713-725
Author(s):  
Eric Dubon ◽  
Juan Matías Sepulcre

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Michael S. Milgram

Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the Zeta and Eta function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.


Sign in / Sign up

Export Citation Format

Share Document