Related papers: The Riemann Hypothesis Emerges in Dynamical Quantu…
The critical line of the Riemann zeta function is studied from a new viewpoint. It is found that the ratio between the zeta function at any zero and the corresponding one at a conjugate point has a certain phase and its absolute value is…
Phase transitions are fundamental in nature. A small parameter change near a critical point leads to a qualitative change in system properties. Across a regular phase transition, the system remains in thermal equilibrium and, therefore,…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…
It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $\Lambda$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical…
We introduce a Hamiltonian to address the Hilbert-P\'olya conjecture. The eigenfunctions of the introduced Hamiltonian, subject to the Dirichlet boundary conditions on the positive half-line, vanish at the origin by the nontrivial zeros of…
A proof of the Riemann hypothesis using the reflection principle is presented.
We present the results of numerical experiments in connection with the Riesz and Hardy-Littlewood criteria for the truth of the Riemann Hypothesis (RH). The coefficients c_k of the Pochammer's expansion for the reciprocal of the Riemann…
In 1859, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\alpha+i\beta$ of the zeta function, defined by: $$\zeta(s) =\displaystyle \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real…
In his foundational book, Edwards introduced a unique "speculation" regarding the possible theoretical origins of the Riemann Hypothesis, based on the properties of the Riemann-Siegel formula. Essentially Edwards asks whether one can find a…
In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with $N$ components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the…
The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number…
We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of…
Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point,…
The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so that the assertion that all its…
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly…
Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…