Related papers: Finite-zone PT-potentials

In this paper we find explicit conditions on the periodic PT-symmetric complex-valued potential q for which the number of gaps in the real part of the spectrum of the one-dimensional Schrodinger operator L(q) is finite.

A way to derive an explicit formulae in terms of the potentials, if they are finite-gap, for the solutions of spectral problems and corresponding algebraic curves is presented.

The class of periodic-finite-type shifts (PFT's) is a class of sofic shifts that strictly includes the class of shifts of finite type (SFT's), and the zeta function of a PFT is a generating function for the number of periodic sequences in…

We study the factorization of the PT symmetric Hamiltonian. The general expression for the superpotential corresponding to the PT symmetric potential is obtained and explicit examples are presented.

We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.

The theory of finite automata applies to the study on relations of multiple zeta values.

We show that formulas differing from classical analogues of rational trace formulas for algebraic-geometric potentials occur in the theory of finite-gap integration of spectral equations. The new formulas contain transcendental modular…

We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.

I give a formula for the zeta function of a projective toric hypersurface over a finite field and estimate its Newton polygon. As an application this formula allows us to compute the exact number of rational points on the families of…

We use the asymptotic expansion of the heat trace to express all residues of spectral zeta functions as regularized sums over the spectrum. The method extends to those spectral zeta functions that are localized by a bounded operator.

We introduce a new method which enables us to calculate the coefficients of the poles of local zeta functions very precisely and prove some explicit formulas. Some vanishing theorems for the candidate poles of local zeta functions will be…

This note contains a short proof of the functional equation for the zeta function.

The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.

We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite graph. Furthermore, we present a determinant expression for…

This paper considers some infinite series involving the Riemann zeta function.

In this paper, we define edge zeta functions for spherical buildings associated with finite general linear groups. We derive elegant formulas for these zeta functions and reveal patterns of eigenvalues of these buildings, by introducing and…

In this paper, we give an overview of the various general methods in computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo $p^m$ of the zeta function of a…

We introduce and study new versions of polylogarithms and a zeta function on a completion of $\mathbb F_q (x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for $\mathbb F_q$-linear functions.

The aim of this paper is to describe explicitly the poles of the meromorphic continuation of the Igusa local zeta function associated to several polynomials. Using resolution of singularities is possible to express the Igusa's local zeta…

In a recent paper Z\'u\~niga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a…