Related papers: Finite-zone PT-potentials

This note examines Gross-Pitaevskii equations with PT-symmetric potentials of the Wadati type: $V=-W^2+iW_x$. We formulate a recipe for the construction of Wadati potentials supporting exact localised solutions. The general procedure is…

From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to…

In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions,…

I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations.

In this manuscript, we give effective methods for computing the zeta function of maximal orders on surfaces.

We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional…

We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

We introduce and study a ``level two'' analogue of finite multiple zeta values. We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A…

In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.

The finite amplitude method is a feasible and efficient method for the linear response calculation based on the time-dependent density functional theory. It was originally proposed as a method to calculate the strength functions. Recently,…

In this paper, we study some properties of multivariate gamma function and zonal polynomials.

A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

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…

In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal…

Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in…

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric…

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.