Related papers: Quantum Spin Chains and Riemann Zeta Function with…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the…
Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At lattice distance m,…
The research shows that Riemann proved that all of zeros of Riemann's zeta function are on $\sigma=1/2$ based on the functional equation \begin{align*} \pi^{-\frac{s}{2}}\Gamma \left( \frac{s}{2} \right) \zeta(s)&={\frac{1}{s(s-1)} +…
We survey some of the universality properties of the Riemann zeta function $\zeta(s)$ and then explain how to obtain a natural quantization of Voronin's universality theorem (and of its various extensions). Our work builds on the theory of…
We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings (a model previously studied by approximate strong-disorder RG). We find that, at least for sufficiently large spin $S$, the ground state has…
The Riemann Hypothesis can be reformulated as statements about the eigenvalues of certain matrices whose entries are defined in terms of the Taylor coefficients of the zeta function. These eigenvalues exhibit interesting visual patterns…
The main result of the paper is a definition of possible ways of the confirmation of the Riemann hypothesis based on the properties of the vector system of the second approximate equation of the Riemann Zeta function. The paper uses a…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to…
We prove some new bounds for the maximum of Riemann zeta-function on very short segments of the critical line. All the theorems are based on the Riemann hypothesis.
In this paper, some new results are reported for the study of Riemann zeta function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$ expressed in a generalized Euler product only involving prime numbers. Particularly, some…
We study the correlation functions of $SU(n)$ $n>2$ invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at…
We study thermodynamic properties of the one-dimensional Heisenberg ferrimagnet with antiferromagnetically exchange-coupled two kinds of spins 1 and 1/2. The specific heat and the magnetic susceptibility are calculated employing a modified…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.
The properties of several functions are employed to investigate the zeros of the Riemann zeta function $\zeta(a+bi)$ $(0<a<1, b\neq 0)$. If the zeros of the zeta function have not the form $\frac{1}{2}+ib$ where $i=\sqrt{-1}$, we derive a…
We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta…