相关论文: The zeros and poles of the partition function

The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the polynomial is related to phase transitions, and plays an important role in the design…

We use the path integral approach to a two-dimensional noncommutative harmonic oscillator to derive the partition function of the system at finite temperature. It is shown that the result based on the Lagrangian formulation of the problem,…

Simple calculations indicate that the partition function for a black hole is defined only if the temperature is fixed on a finite boundary. Consequences of this result are discussed. (Contribution to the Proceedings of the Lanczos Centenary…

We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…

Let $p(z)=a_0+a_1z+a_2z^2+a_3z^3+\cdots+a_nz^n$ be a polynomial of degree $n,$ where the coefficients $a_j,$ $j \in \{0,1,2,\cdots n\},$ may be complex. We impose some restriction on the coefficients of the real part of the given polynomial…

We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results…

Ramanujan investigated maximal order for the number of divisors function by introducing some notion such as (superior) highly composite numbers. He also studied maximal order for other arithmetic functions including the sum of powers of…

A new integral representation for the Riemann zeta function is derived. This representation covers the important region of the complex plane where the real part of the argument of the function lies between 0 and 1. Using this…

The partition function of a two dimensional Abelian gauge model reproducing magnetic vortices is discussed in the harmonic approximation. Classical solutions exhibit conformal invariance, that is broken by statistical fluctuations, apart…

One key element to calculate thermodynamical properties for a black hole is the partition function. In this paper we have incorporated the idea of a two dimensional area in a noncommutative space and were able to calculate the partition…

The dynamics of a nearly-AdS2 spacetime with boundaries is reduced to two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We…

Several results are obtained concerning multiplicities of zeros of the Riemann zeta-function $\zeta(s)$. They include upper bounds for multiplicities, showing that zeros with large multiplicities have to lie to the left of the line $\sigma…

We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat…

The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…

Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for…

In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function $\zeta(s)$ (and other L-functions) using Montgomery's pair correlation approach. We use semidefinite programming to improve upon numerous…

We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by…

We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…

The number of partitions of $n$ wherein odd parts are distinct and even parts are unrestricted, often denoted by $pod(n)$. In this paper, we provide linear recurrence relations for $pod(n)$, and the connections of $pod(n)$ with other…

We continue to investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence begun in arxiv:0708.0645. We derive the master matrix of the $(2,1)$…