Related papers: Zeta functions of quantum graphs
By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…
Neutral atom technology has steadily demonstrated significant theoretical and experimental advancements, positioning itself as a front-runner platform for running quantum algorithms. One unique advantage of this technology lies in the…
This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals…
The present essay aims at investigating whether and how far an algebraic analysis of the Zeta Function and of the Riemann Hypothesis can be carried out. Of course the well-established properties of the Zeta Function, explored in depth in…
Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we…
The paper deals with the analytic entire function Chi(s) closely related to Riemann Zeta Function Zeta(s). A formula is obtained for Chi(s) essentially within the so-called critical strip. This is achieved by applying Cauchy integral…
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
In this paper, we study graph-theoretic analogies of the Mertens' theorems by using basic properties of the Ihara zeta-function. One of our results is a refinement of a special case of the dynamical system Mertens' second theorem due to…
To a finite, connected, unoriented graph of Betti-number g>=2 and valencies >=3 we associate a finitely summable, commutative spectral triple (in the sense of Connes), whose induced zeta functions encode the graph. This gives another…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations of the two-particle Laplacian including such interactions…
Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of…
Curves over finite fields are of great importance in cryptography and coding theory. Through studying their zeta-functions, we would be able to find out vital arithmetic and geometric information about them and their Jacobians, including…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…
Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…
The purpose of this paper is to present a quantum statistical theory of 2-dimensional vortex gas based on the generalized Hamiltonian dynamics recently developed. The quantized spectrum is evaluated for a pair of vortex on the basis of the…
Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…
We present drawings on the complex plane of the lines Im(zeta(s))=0 and Re(zeta(s))=0. This allow to illustrate many properties of the zeta function of Riemann. This is an expository paper. It does not pretend to prove any new result about…
We discuss modifications in the integral representation of the Riemann zeta-function that lead to generalizations of the Riemann functional equation that preserves the symmetry $s\to (1-s)$ in the critical strip. By modifying one integral…