Results 1 to 10 of about 68,409 (246)

New versions of the Nyman-Beurling criterion for the Riemann hypothesis [PDF]

International Journal of Mathematics and Mathematical Sciences, 2002
Let ρ(x)=x−[x], χ=χ(0,1), λ(x)=χ(x)logx, and M(x)=ΣK≤x μ(k), where μ is the Möbius function.
Luis Báez-Duarte
doaj   +2 more sources

Physics of the Riemann Hypothesis [PDF]

, 2011
Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics.
Ablowitz, M. J., Aczel, A. D., Alfaro, V. D., Arnol’d, V. I., Berry, M. V., Berry, M. V., Bhaduri, R. K., Bohigas, O., Bohigas, O., Borwein, P., Brack, M., Böhm, A., Celletti, A., Chadan, K., Cipra, B., Cvitanović, P., David A. W. Hutchinson, de la Vallée-Poussin, C. J., Dickson, L. E., Drake, S., Dyson, F., Dániel Schumayer, Eckhardt, B., Einstein, A., Elizalde, E., Elizalde, E., Euler, L., Flügge, S., Gelfand, I. M., Gutzwiller, M. C., Hadamard, J., Hadamard, J., Hardy, G. H., Hardy, G. H., Hejhal, D. A., Hejhal, D. A., Huang, K., Ivic, A., Joffily, S., Julia, B., Kanemitsu, S., Kotnik, T., Lapidus, M. L., Mehta, M. L., Montgomery, H. L., Newton, R. G., Press, W. H., Ribenboim, P., Ribenboim, P., Riemann, B., Riemann, B., Schnirelman, A. I., Stöckmann, H.-J., Titchmarsh, E. C., Vardi, I., Xianxi, D.   +55 more
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Chebyshev's bias and generalized Riemann hypothesis [PDF]

, 2011
It is well known that $li(x)>\pi(x)$ (i) up to the (very large) Skewes' number $x_1 \sim 1.40 \times 10^{316}$ \cite{Bays00}. But, according to a Littlewood's theorem, there exist infinitely many $x$ that violate the inequality, due to the specific ...
Alamadhi, Adel, Planat, Michel, Solé, Patrick   +2 more
core   +5 more sources

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

The Generalized Riemann Hypothesis on elliptic complex fields

AIMS Mathematics, 2023
In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function $ L(s, \chi) $ in the corresponding complex plane. The key to this article is to discover the limiting case of the
Xian Hemingway
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

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
doaj   +1 more source

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
doaj   +1 more source

The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation

Journal of Nigerian Society of Physical Sciences, 2022
The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch, Adejimi A. Adeniji, Lukman O. Salaudeen   +2 more
doaj   +1 more source