Results 21 to 30 of about 48,716 (213)

A stochastic interpretation of the Riemann zeta function. [PDF]

Proc Natl Acad Sci U S A, 1993
We give a stochastic process for which the terms of the Riemann zeta function occur as the probability distributions of the elementary random variables of the process.
Alexander KS, Baclawski K, Rota GC.
europepmc   +4 more sources

Some identities related to Riemann zeta-function

Journal of Inequalities and Applications, 2016
It is well known that the Riemann zeta-function ζ ( s ) $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to study the computational problem of one kind of
Lin Xin
doaj   +3 more sources

THEOREM ON THE “UNIVERSALITY” OF THE RIEMANN ZETA-FUNCTION

Mathematics of the USSR-Izvestiya, 1975
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Voronin
semanticscholar   +3 more sources

Explicit zero-free regions for the Riemann zeta-function [PDF]

Research in Number Theory, 2022
We prove that the Riemann zeta-function ζ(σ+it)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
Michael J. Mossinghoff, T. Trudgian, Andrew Yang   +2 more
semanticscholar   +1 more source

Correlations of the Riemann zeta function [PDF]

Mathematika, 2023
Assuming the Riemann hypothesis, we investigate the shifted moments of the zeta function Mα,β(T)=∫T2T∏k=1mζ12+i(t+αk)2βkdt$$\begin{equation*} \hspace*{24.5pt}M_{{\bm \alpha}, {\bm \beta}} (T) = \int _T^{2T} \prod _{k = 1}^m {\left|\zeta \left(\tfrac{1}{2}
Michael J. Curran
semanticscholar   +1 more source

Explicit bounds for the Riemann zeta function and a new zero-free region [PDF]

Journal of Mathematical Analysis and Applications, 2023
We prove that $|\zeta(\sigma+it)|\le 70.7 |t|^{4.438 (1-\sigma)^{3/2}}\log^{2/3}|t|$ for $1/2\le\sigma\le 1$ and $|t|\ge 3$. As a consequence, we improve the explicit zero-free region for $\zeta(s)$, showing that $\zeta(\sigma+it)$ has no zeros in the ...
C. Bellotti
semanticscholar   +1 more source

Counting zeros of the Riemann zeta function [PDF]

Journal of Number Theory, 2021
In this article, we show that | N ( T ) − T 2 π log ⁡ ( T 2 π e ) | ≤ 0.1038 log ⁡ T + 0.2573 log ⁡ log ⁡ T + 9.3675 where N ( T ) denotes the number of non-trivial zeros ρ, with 0 Im ( ρ ) ≤ T , of the Riemann zeta function.
Elchin Hasanalizade, Quanli Shen, PENG-JIE Wong   +2 more
semanticscholar   +1 more source

Shifted moments of the Riemann zeta function [PDF]

Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2022
In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concerning sharp upper bounds for the $2k$ th moments of the Riemann zeta ...
Nathan Ng, Quanli Shen, PENG-JIE Wong
semanticscholar   +1 more source

Aspects of the screw function corresponding to the Riemann zeta‐function [PDF]

Journal of the London Mathematical Society, 2022
We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function.
Masatoshi Suzuki
semanticscholar   +1 more source

Four Variants of Riemann Zeta Function

Mathematics, 2022
By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
doaj   +1 more source