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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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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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On Robin’s criterion for the Riemann Hypothesis
Notes on Number Theory and Discrete Mathematics, 2021 Robin’s criterion says that the Riemann Hypothesis is equivalent to \[\forall n\geq 5041, \ \ \frac{\sigma(n)}{n}\leq e^{\gamma}\log_2 n,\] where \sigma(n) is the sum of the divisors of n, \gamma represents the Euler–Mascheroni constant, and \log_i ...
Safia Aoudjit, Djamel Berkane, P. Dusart
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The Riemann hypothesis and tachyonic off-shell string scattering amplitudes
European Physical Journal C: Particles and Fields, 2022 The study of the $$\mathbf{4}$$ 4 -tachyon off-shell string scattering amplitude $$ A_4 (s, t, u) $$ A 4 ( s , t , u ) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “
Carlos Castro Perelman
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Traces of certain integral operators related to the Riemann hypothesis
AIMS Mathematics, 2023 We prove the existence of a nontrivial singular trace $ \tau $ defined on an ideal $ \mathcal{J} $ closed with respect to the logarithmic submajorization such that $ \tau(A_\rho(\alpha)) = 0 $, where $ A_\rho(\alpha):L^{2}(0, 1)\to L^{2}(0, 1) $, $ {[A_ ...
Alfredo Sotelo-Pejerrey
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Symmetries and the Riemann Hypothesis [PDF]
Advanced Studies in Pure Mathematics, 2008 Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis.
Lin Weng
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Analogues of the Robin–Lagarias criteria for the Riemann hypothesis [PDF]
, 2020 Robin's criterion states that the Riemann hypothesis is equivalent to $\sigma(n) < e^\gamma n \log\log n$ for all integers $n \geq 5041$, where $\sigma(n)$ is the sum of divisors of $n$ and $\gamma$ is the Euler-Mascheroni constant.
L. Washington, Ambrose Yang
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Analyzing Riemann's hypothesis
, 2022 In this paper we perform a detailed analysis of Riemann's hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation $ζ(s) = 2^{s}π^{s-1}\sin{(\displaystyle πs/2)}Γ(1-s)ζ(1-s)$ for complex numbers $s$ such that $0<{\rm Re(s)}<1$ and the reduction to the absurd method where we use an analytical ...
Orus-Lacort, Mercedes +2 more
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Toward the Unification of Physics and Number Theory [PDF]
Reports in Advances of Physical Sciences, 2019 This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure.
Klee Irwin
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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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