Results 11 to 20 of about 68,409 (246)
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.
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The Riemann zeros as spectrum and the Riemann hypothesis [PDF]
Symmetry, 2019 We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers.
Sierra, Germán
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Thoughts on the Riemann hypothesis [PDF]
The Mathematical Intelligencer, 2003 The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of ...
Chaitin, G. J.
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, 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.
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Chronic insomnia, REM sleep instability and emotional dysregulation: A pathway to anxiety and depression? [PDF]
J Sleep ResSummary 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 +13 more
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Journal of Number Theory, 1996 AbstractIt has been shown by Wan [W1] that a version of the Riemann hypothesis for characteristicpvalued zeta functions, due to D. Goss, is satisfied forFq[T], withq=pbeing prime. We present another proof of this result.
Javier Diaz-Vargas
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Disproof of the Riemann Hypothesis [PDF]
, 2021 We define the function $\upsilon(x) = \frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log (x + C \times \sqrt{x} \times \log \log \log x)} - 1$ for some positive constant $C$ independent of $x$. We prove that the Riemann hypothesis is false when there exists some number $y \geq 13.1$ such that for all ...
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The Riemann hypothesis is false
, 2022 Let Theta be the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate in this note that Theta must be at least 3/4. This disproves the Riemann hypothesis, which asserts that Theta = 1/2.
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The Riemann Hypothesis Is True [PDF]
, 2021 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 $\frac{1}{2}$. The Riemann hypothesis belongs to the David Hilbert's list of 23 unsolved problems. Besides, it is one of the Clay Mathematics Institute's Millennium Prize Problems.
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Counterexample of the Riemann Hypothesis [PDF]
, 2022 Under the assumption that the Riemann hypothesis is true, von Koch deduced the improved asymptotic formula $\theta(x) = x + O(\sqrt{x} \times \log^{2} x)$, where $\theta(x)$ is the Chebyshev function. We obtain a result which contradicts this asymptotic formula. By contraposition, we deduce that the Riemann hypothesis is false.
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