Results 101 to 110 of about 1,625,058 (297)
A Geometric Proof of Riemann Hypothesis [PDF]
arXiv, 2003 Beginning from the formal resolution of Riemann Zeta function, by using the formula of inner product between two infinite-dimensional vectors in the complex space, the author proved the world's baffling problem -- Riemann hypothesis raised by German mathematician B. Riemann in 1859.
arxiv
Journal of Sleep Research, EarlyView.Summary Insomnia is highly prevalent and associated with serious health issues. Despite the negative impact of poor sleep on mind and body, most people do not seek treatment. This study aimed to examine the strategies used to improve sleep in the general population with a particular focus on music.
Rasmus Møller Buus +2 more
wiley +1 more source
The Nicolas criterion for the Riemann Hypothesis [PDF]
, 2021 For every prime number $p_{n}$, we define the sequence $X_{n} = \prod_{q \leq p_{n}} \frac{q}{q-1} - e^{\gamma} \times \log \theta(p_{n})$, where $\theta(x)$ is the Chebyshev function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. The Nicolas theorem states that the Riemann hypothesis is true if and only if the $X_{n} > 0$ holds for ...
openaire +7 more sources
A Connection between the Riemann Hypothesis and Uniqueness of the Riemann zeta function [PDF]
arXiv, 2016 In this paper, we give a connection between the Riemann hypothesis and uniqueness of the Riemann zeta function and an analogue for L-functions.
arxiv
An investigation of the non-trivial zeros of the Riemann zeta function
, 2020 The zeros of the Riemann zeta function outside the critical strip are the so-called trivial zeros. While many zeros of the Riemann zeta function are located on the critical line $\Re(s)=1/2$, the non-existence of zeros in the remaining part of the ...
Heymann, Yuri
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Sleep Health and White Matter Integrity in the UK Biobank
Journal of Sleep Research, EarlyView.ABSTRACT Many people experience impaired sleep health, yet knowledge about its neurobiological correlates is limited. As previous studies have found associations between white matter integrity and several sleep traits, white matter integrity could be causally implicated in poor sleep health.
Roxana Petri +8 more
wiley +1 more source
The Riemann Hypothesis and the possible proof [PDF]
arXiv, 2014 The Riemann Hypothesis is not proved yet and this article gives a possible proof for the hypothesis which confirms that the only possible nontrivial zeros of the Riemann zeta-function has its real value equal to 1/2. From the result, the application of the Riemann Hypothesis will be certified, e.g. research on prime numbers.
arxiv
Dreaming of Better Treatments: Advances in Drug Development for Sleep Medicine and Chronotherapy
Journal of Sleep Research, EarlyView.ABSTRACT Throughout history, the development of new sleep medicines has been driven by progress in our understanding of the mechanisms underlying sleep. Ancient civilisations used their understanding of the sedative nature of natural herbs and compounds to induce sleep.
Brooke A. Prakash +5 more
wiley +1 more source
On Generalized Riemann Hypothesis
, 2018 This work as a natural followup to our previous work on the Riemann hypothesis. In this work we shall demonstrate our approach in the previous work can resolve the generalized Riemann hypothesis for an non-principal primitive Dirichlet as well.Comment:
Zhang, Ruiming
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