Related papers: The alien in the Riemann zeta function
Our Cycle 0 ALMA observations confirmed that the Boomerang Nebula is the coldest known object in the Universe, with a massive high-speed outflow that has cooled significantly below the cosmic background temperature. Our new CO 1-0 data…
Recent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed…
The perturbed Friedmann-Lemaitre-Robertson-Walker models allow many different possibilities for the 3-manifold of the comoving spatial section of the Universe. It used to be thought that global properties of the spatial section, including…
We derive explicit upper bounds for the Riemann zeta-function $\zeta(\sigma + it)$ on the lines $\sigma = 1 - k/(2^k - 2)$ for integer $k \ge 4$. This is used to show that the zeta-function has no zeroes in the region $$\sigma > 1 -…
While non-rotating black-hole solutions are well known in Einstein--\ae{}ther gravity, no axisymmetric solutions endowed with Killing horizons have been so far found outside of the slowly rotating limit. Here we show that the Kerr spacetime…
Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10^{-4} pc till 100 pc. Secondly, the galaxy distribution has been observed to be fractal in…
All the relativistic cosmological models of the universe, except Einstein's static model, imply that the 3-space of the spacetime of the universe is also expanding apart from the matter and the radiation in it. However, there is no…
We consider the real part $\Re(\zeta(s))$ of the Riemann zeta-function $\zeta(s)$ in the half-plane $\Re(s) \ge 1$. We show how to compute accurately the constant $\sigma_0 = 1.19\ldots$ which is defined to be the supremum of $\sigma$ such…
We point out that the {\em spacetime void} inferred by Castro[J. Math. Phys. 49, 042501, (2008)] results from his choice of a discontinuous radial gauge. Further since the integration constant $\alpha_0 = 2M_0$ ($G=c=1$) occurring in the…
In this work, which follows a series of studies on the higher-dimensional steady state universe idea and prepared for Professor Tekin Dereli's Festschrift, we show the influence of the dynamical internal (unobservable) space on the…
The Riemann hypothesis is identified with zeros of ${\cal N}=4$ supersymmetric gauge theory four-point amplitude. The zeros of the $\zeta(s)$ function are identified with th complex dimension of the spacetime, or the dimension of the…
We propose a toy model of a spherical universe made up of an exotic dark gas with temperature $T$ in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy…
In homogeneous cosmological models the wavelength $\lambda$ of a photon exchanged between two fundamental observers changes in proportion to expansion of the space $D$ between them, so $\Delta\log(\lambda / D) = 0$. This is exactly the same…
The Einstein-Skyrme system is understood to defy the "no hair" conjecture by possessing black-hole solutions with fractional baryon number outside the event horizon. In this article, we extend the study of the Skyrme system to teleparallel…
In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the…
Withdrawn; conclusion that the singularity is strong is incorrect.
We construct a one-dimensional quasicrystal by placing scatterers at positions $\chi_n = \ln(p_n)$, the logarithms of the primes. This map compresses the primes to approximately constant density and yields a Fourier transform that is…
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
We present and describe an exact solution of Einstein's equations which represents a snapping cosmic string in a vacuum background with a cosmological constant $\Lambda$. The snapping of the string generates an impulsive spherical…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…