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Riemann hypothesis

Journal of Applied Mathematics and Physics, 2019
This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions.
Durmagambetov, A.
core   +3 more sources

The Riemann Hypothesis

, 2020
This work was supported by another researcher that shall be included as an author after his approval.
Richard Beals, Roderick S. C. Wong
  +13 more sources

Sleep Reactivity Amplifies the Impact of Pre-Sleep Cognitive Arousal on Sleep Disturbances. [PDF]

J Sleep Res
This study investigates how sleep reactivity moderates the ‘stress‐pre‐sleep arousal‐sleep’ pathway in university students. At the within‐individual level, both high and low sleep‐reactive groups showed increased pre‐sleep cognitive arousal and sleep disruptions in response to elevated daily stress.
Shaif NAS, Lim J, Reffi AN, Chee MWL, Massar SAA, Ong JL.   +5 more
europepmc   +2 more sources

Chronic insomnia, REM sleep instability and emotional dysregulation: A pathway to anxiety and depression? [PDF]

J Sleep Res
Summary The world‐wide prevalence of insomnia disorder reaches up to 10% of the adult population. Women are more often afflicted than men, and insomnia disorder is a risk factor for somatic and mental illness, especially depression and anxiety disorders.
Riemann D, Dressle RJ, Benz F, Spiegelhalder K, Johann AF, Nissen C, Hertenstein E, Baglioni C, Palagini L, Krone L, Perlis ML, Domschke K, Berger M, Feige B.   +13 more
europepmc   +2 more sources

Riemann Hypothesis [PDF]

, 2023
Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function.
  +7 more sources

The Riemann Hypothesis [PDF]

, 2021
In mathematics, the Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. In 1915, Ramanujan proved that under the assumption of the Riemann Hypothesis, the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all ...
  +6 more sources

Two generalizations of Liouville λ function [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
We study the properties of two classes of functions λₖ and ~λₖ that generalize the Liouville λ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of λₖ and ...
André Pierro de Camargo
doaj   +1 more source

Black holes, quantum chaos, and the Riemann hypothesis

SciPost Physics Core, 2021
Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for
Panagiotis Betzios, Nava Gaddam, Olga Papadoulaki
doaj   +1 more source

Riemann hypothesis and Zeta-Function

Bibechana, 2018
No abstract available.
Mani Raj Bhattrai
doaj   +3 more sources

An Analytical and Numerical Detour for the Riemann Hypothesis

Information, 2021
From the functional equation F(s)=F(1−s) of Riemann’s zeta function, this article gives new insight into Hadamard’s product formula. The function S1(s)=d(lnF(s))/ds and its family of associated Sm functions, expressed as a sum of rational fractions, are ...
Michel Riguidel
doaj   +1 more source