Related papers: Generating weighted Hurwitz numbers
We define cut-and-join operator in Hurwitz theory for merging of two branching points of arbitrary type. These operators have two alternative descriptions:(i) they have the GL characters as eigenfunctions and the symmetric-group characters…
We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
Correlation function of twist operators is a natural quantity of interest in two-dimensional conformal field theory (2d CFT) and finds relevance in various physical contexts. For computing twist operator correlators associated with generic…
The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one…
We construct a family of bilinear differential operators which satisfy certain gauge properties. These operators can be naturally associated with $q$-deformations of classical integrable hierarchies. In particular, we consider the case when…
We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we evaluate those double series. Our main results can be regarded as a certain…
Motivated by results for the HCIZ integral in Part I of this paper, we study the structure of monotone Hurwitz numbers, which are a desymmetrized version of classical Hurwitz numbers. We prove a number of results for monotone Hurwitz…
We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Euler-Zagier-Lerch type and investigate their analytic…
We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the $x-y$ duality for logarithmic topological recursion. We use this family to systematically demonstrate, refine and…
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special…
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value…
We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formul\ae\ of a new type for the generating series of…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbol{\alpha})$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbol{\alpha})$. Then we consider…
The one-matrix model is considered. The generating function of the correlation numbers is defined in such a way that this function coincide with the generating function of the Liouville gravity. Using the Kontsevich theorem we explain that…
We prove sum formulas for double polylogarithms of Hurwitz type, that is, involving a shifting parameter $b$ in the denominator. These formulas especially imply well-known sum formulas for double zeta values, and sum formulas for double…
This paper studies three different ways to assign weights to the lattice points of a convex polytope and discusses the algebraic and combinatorial properties of the resulting weighted Ehrhart functions and their generating functions and…
The classical Hurwitz numbers count the fixed-length transitive transposition factorizations of a permutation, with a remarkable product formula for the case of minimum length (genus $0$). We study the analogue of these numbers for…