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Shifted fourth moment of the Riemann zeta-function

Acta Mathematica Hungarica
Volume/Issue:
Volume 137: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-012-0203-x
Author: Shun Shimomura

References [1] Bettin , S. 2010 The second moment of the Riemann zeta-function with unbounded shifts Int. J. Number Theory

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Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 57: Issue 2
DOI:
https://doi.org/10.1556/012.2020.57.2.1460
Author: Antanas Laurinčikas

) s . Moreover, the function ζ ( s, α ) can be analytically continued to the whole complex plane, except for a simple pole at the point s = 1 with residue 1. For α = 1, the Hurwitz zeta-function becomes the Riemann zeta-function ζ ( s ): ζ ( s

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On spectrums of certain harmonic functions attached to the Riemann zeta-function

Acta Mathematica Hungarica
Volume/Issue:
Volume 105: Issue 1-2
DOI:
https://doi.org/10.1023/b:amhu.0000045534.41502.3e
Author: Yuichi Kamiya

Abstract  

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.

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The Mellin transform of the square of Riemann's zeta-function

Periodica Mathematica Hungarica
Volume/Issue:
Volume 42: Issue 1-2
DOI:
https://doi.org/10.1023/a:1015213127383
Author: Matti Jutila
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An observation on the zero-free region of the Riemann zeta-function

Periodica Mathematica Hungarica
Volume/Issue:
Volume 42: Issue 1-2
DOI:
https://doi.org/10.1023/a:1015252708727
Author: Yoichi Motohashi
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On the means of the argument of the Riemann zeta-function on the critical line

Acta Mathematica Hungarica
Volume/Issue:
Volume 58: Issue 1-2
DOI:
https://doi.org/10.1007/bf01903543
Author: L. Groenewald
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Disproof of some conjectures of P. Turán

Acta Mathematica Hungarica
Volume/Issue:
Volume 117: Issue 3
DOI:
https://doi.org/10.1007/s10474-007-6096-4
Author: J. Andersson

Abstract  

We disprove some power sum conjectures of Tur�n that would have implied the density hypothesis of the Riemann zeta-function if true.

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Spectral sets of certain unbounded functions

Acta Mathematica Hungarica
Volume/Issue:
Volume 110: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-006-0006-z
Author: Yuichi Kamiya

Summary  

A. Beurling introduced the concept of spectral sets of unbounded functions to study the possibility of the approximation of those by trigonometric polynomials. We consider spectral sets of unbounded functions in a certain class which contains the square of the Riemann zeta-function as a typical example.

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Explicit representations of the integral containing the error term in the divisor problem

Acta Mathematica Hungarica
Volume/Issue:
Volume 129: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-9219-2
Authors: J. Furuya and Y. Tanigawa

Abstract  

We shall investigate several properties of the integral

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int_1^\infty {t^{ - \theta } \Delta _k \left( t \right) log^j t dt}$$ \end{document}
with a natural number k, a non-negative integer j and a complex variable θ, where Δk(x) is the error term in the divisor problem of Dirichlet and Piltz. The main purpose of this paper is to apply the “elementary methods” and the “elementary formulas” to derive convergence properties and explicit representations of this integral with respect to θ for k = 2.

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On simple zeros of the Reimann zeta-function in short intervals on the critical line

Acta Mathematica Hungarica
Volume/Issue:
Volume 96: Issue 4
DOI:
https://doi.org/10.1023/a:1019767816190
Author: J. Steuding
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