Results 21 to 30 of about 67,838 (152)
On a de Branges space related to the Riemann zeta function
Вестник Самарского университета: Естественнонаучная серияIn a recent article by V.V. Kapustin a de Branges space, whose element is an expression containing the Riemann xi function, was constructed; the canonical system with a diagonal Hamiltonian and the generalized Fourier transform corresponding to the space
Svetlana A. Badonova
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On the long-time asymptotics of the modified Camassa–Holm equation with step-like initial data
European Journal of Applied MathematicsWe study the long-time asymptotics for the solution of the modified Camassa–Holm (mCH) equation with step-like initial data. \begin{align*} &m_{t}+\left (m\left (u^{2}-u_{x}^{2}\right )\right )_{x}=0, \quad m=u-u_{xx}, \\[3pt] & {u(x,0)=u_0(x)\to ...
Engui Fan, Gaozhan Li, Yiling Yang
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On the zeros of Riemann's Xi Function
, 2023 We consider Riemann's Xi function $ξ(s)$ which is evaluated at $s = \frac{1}{2} + σ+ i ω$, given by $ξ(\frac{1}{2} + σ+ i ω)= E_{pω}(ω)$, where $σ, ω$ are real and compute its inverse Fourier transform given by $E_p(t)$. We study the properties of $E_p(t)$ and a promising new method is presented which could be used to show that the Fourier Transform of
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A canonical system of differential equations arising from the Riemann zeta-function [PDF]
, 2016 This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\Theta_\omega(z)=\xi(1/2-\omega-iz)/\xi(1/2+\omega-iz)$, where $\omega>0$ is a real parameter and $\xi(s)$ is the Riemann xi-function. The
Suzuki, Masatoshi
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A monotonicity property of Riemann’s $${\varvec{\xi }}$$ function along certain curves
Indian Journal of Pure and Applied Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On special Riemann xi function formulae of Hardy involving the digamma function [PDF]
Acta Scientiarum Mathematicarum, 2021 We consider some properties of integrals considered by Hardy and Koshliakov, and which have also been further extended recently by Dixit. We establish a new general integral formula from some observations about the digamma function. We also obtain lower and upper bounds for Hardy's integral through properties of the digamma function.
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, EarlyView.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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Riemann Hypothesis proof using Logarithmic derivative of Riemann Xi function
, 2021 easy ...
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Contributions to Plasma Physics, EarlyView.ABSTRACT Warm dense matter (WDM) is a complex state, where quantum effects, thermal excitations, and strong interparticle correlations coexist. Understanding its microscopic composition and medium‐induced modifications of atomic and molecular properties is essential for planetary modeling, fusion research, and high‐energy‐density experiments.
L. T. Yerimbetova +4 more
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Riemann Hypothesis proof using Hadamard product and Riemann xi function
, 2021 Easy proof.
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