Results 1 to 10 of about 72,493 (237)

The inverses of tails of the Riemann zeta function [PDF]

Journal of Inequalities and Applications, 2018
We present some bounds of the inverses of tails of the Riemann zeta function on ...
Donggyun Kim, Kyunghwan Song
doaj   +4 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, Timothy S. Trudgian, Andrew Yang   +2 more
openalex   +3 more sources

Jensen polynomials for the Riemann zeta function and other sequences. [PDF]

Proc Natl Acad Sci U S A, 2019
Significance The Pólya–Jensen criterion for the Riemann hypothesis asserts that RH is equivalent to the hyperbolicity of certain Jensen polynomials for all degrees d≥1 and all shifts n.
Griffin M, Ono K, Rolen L, Zagier D.
europepmc   +3 more sources

Extreme values of derivatives of the Riemann zeta function. [PDF]

Mathematika, 2022
It is proved that if T is sufficiently large, then uniformly for all positive integers ℓ⩽(logT)/(log2T)$\ell \leqslant (\log T) / (\log _2 T)$ , we have maxT⩽t⩽2Tζ(ℓ)1+it⩾eγ·ℓℓ·(ℓ+1)−(ℓ+1)·log2T−log3T+O(1)ℓ+1,\begin{eqnarray*} &&\hspace*{13pc} \max _{T ...
Yang D.
europepmc   +3 more sources

On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function [PDF]

Complex Variables and Elliptic Equations, 2020
In this paper, we prove that ζ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in over the ring of polynomials in , are nonnegative integers.
Qiongyan Wang, Manli Liu, Nan Li
openalex   +3 more sources

Scalar modular bootstrap and zeros of the Riemann zeta function [PDF]

Journal of High Energy Physics, 2022
Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of
Nathan Benjamin, Cyuan-Han Chang
doaj   +2 more sources

Counting zeros of the Riemann zeta function [PDF]

Journal of Number Theory, 2021
Elchin Hasanalizade, Quanli Shen, Peng‐Jie Wong   +2 more
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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

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