scholarly journals On complex zeros off the critical line for non-monomial polynomial of zeta-functions

2016 ◽  
Vol 284 (1-2) ◽  
pp. 23-39 ◽  
Author(s):  
Takashi Nakamura ◽  
Łukasz Pańkowski
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Complex Zeros

scholarly journals Zeros of quadratic zeta-functions on the critical line

1995 ◽  
Vol 69 (1) ◽  
pp. 21-38 ◽  
Author(s):  
A. Sankaranarayanan
Keyword(s):  
Critical Line ◽  
Zeta Functions

scholarly journals On certain sums over ordinates of zeta-zeros II

2019 ◽  
Author(s):  
Andriy Bondarenko ◽  
Aleksandar Ivić ◽  
Eero Saksman ◽  
Kristian Seip
Keyword(s):  
Analytic Continuation ◽  
Critical Line ◽  
Laurent Expansion ◽  
Second Moment ◽  
International Audience ◽  
Complex Zeros ◽  
Gamma S

International audience Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function $G(s) :=\sum_{\gamma >0} {\gamma}^{-s}$ to the left of the line $\Re{s} = −1 $ is investigated, and its Laurent expansion at the pole s = 1 is obtained. Estimates for the second moment on the critical line $\int_{1}^{T} {| G (\frac{1}{2} + it) |}^2 dt $ are revisited. This paper is a continuation of work begun by the second author in [Iv01].

scholarly journals The fourth moment of individual Dirichlet L-functions on the critical line

2020 ◽  
Author(s):  
Berke Topacogullari
Keyword(s):  
Critical Line ◽  
Power Saving ◽  
Zeta Functions ◽  
Number Fields ◽  
Fourth Moment ◽  
Quadratic Number ◽  
Second Moment ◽  
Dirichlet Characters ◽  
Asymptotic Formulae ◽  
Special Cases

Abstract We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give uniform asymptotic formulae for the fourth moment of individual Dirichlet L-functions and for the second moment of Dedekind zeta functions of quadratic number fields on the critical line.

scholarly journals A note on the gaps between zeros of Epstein's zeta-functions on the critical line

2017 ◽  
Vol 57 (2) ◽  
pp. 235-253
Author(s):  
Stephan Baier ◽  
Srinivas Kotyada ◽  
Usha Keshav Sangale
Keyword(s):  
Critical Line ◽  
Zeta Functions

Mean values of certain zeta-functions on the critical line

1990 ◽  
Vol 29 (4) ◽  
pp. 351-360
Author(s):  
A. Ivic ◽  
A. Perelli
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Mean Values
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