Results 31 to 40 of about 67,078 (181)

Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis

Information, 2020
This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
doaj   +1 more source

Physics of the Riemann Hypothesis

, 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
core   +1 more source

Large gaps between consecutive zeros of the Riemann zeta-function. II

, 2013
Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average ...
Bui, H. M.
core   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy

Mathematics
New analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one.
Rogelio Tomás García
doaj   +1 more source

Development of a New Zeta Formula and Its Role in Riemann Hypothesis and Quantum Physics

Mathematics, 2023
In this study, we investigated a new zeta formula in which the zeta function can be expressed as the sum of an infinite series of delta and cosine functions.
Saadeldin Abdelaziz, Ahmed Shaker, Mostafa M. Salah   +2 more
doaj   +1 more source

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
core  

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Toward an idiographic understanding of the role of sleep‐mood dynamics in adolescents' internalizing symptoms

JCPP Advances, EarlyView.
Abstract Background Adolescence is marked by increased vulnerability to sleep disturbances and mood disorders. Understanding how day‐to‐day changes in sleep and mood are linked within the same individual is crucial for clarifying sleep's role in emerging internalizing disorders. However, the extent to which an adolescent's fluctuations in sleep predict
Konstantin Drexl, Setareh Ranjbar, Sébastien Urben, Kerstin Jessica Plessen, Jennifer Glaus   +4 more
wiley   +1 more source

New versions of the Nyman-Beurling criterion for the Riemann hypothesis

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   +1 more source