Related papers: Infinite Product Representation for the Szego Kern…

We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series…

We compute the Szeg\"o kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not…

We generalize Nagel's formula for the Szeg\"o kernel and use it to compute the Szeg\"o kernel on a class of noncompact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also…

A wealth of information on multiloop string amplitudes is encoded in fermionic two-point functions known as Szeg\"o kernels. In this paper we show that cyclic products of any number of Szeg\"o kernels on a Riemann surface of arbitrary genus…

Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…

We obtain the product for the auxiliary function $\mathop{\mathcal R}(s)$ and study some related functions as its phase $\omega(t)$ at the critical line. The function $\omega(t)$ determines the zeros of $\zeta(s)$ on the critical line. We…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szeg\"o kernel of the disk bundle over a noncompact K\"ahler manifold. In particular we compute the Szeg\"o kernel…

The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovasz to determine the Shannon capacity of the pentagon; to show a direct sum theorem for…

In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C^2. Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

The cyclic product of an arbitrary number of Szeg\"o kernels for even spin structure $\delta$ on a compact higher-genus Riemann surface $\Sigma$ may be decomposed via a descent procedure which systematically separates the dependence on the…

We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism $(X,S)\twoheadrightarrow(Y,T)$, we can establish emulation by a…

In this paper, we propose and analyze a product integration method for the second-kind integral equation with weakly singular and continuous kernels on the unit sphere $\mathbb{S}^2$. We employ quadrature rules that satisfy the…

Let G be a group which has for all n a finite number r_n(G) of irreducible complex linear representations of dimension n. Let $\zeta(G,s) = \sum_{n=1}^{\infty} r_n(G) n^{-s}$ be its representation zeta function. First, in case G is a…

This work produces a q-analogue of the Cauchi-Szeg\"o integral representation that retrieves a holomorphic function in the matrix ball from its values on the Shilov boundary. Besides that, the Shilov boundary of the quantum matrix ball is…

In recent years, Karr's difference field theory has been extended to the so-called $R\Pi\Sigma$-extensions in which one can represent not only indefinite nested sums and products that can be expressed by transcendental ring extensions, but…

We prove an analogue of Selberg's explicit formula for Motohashi's product (see arXiv:1104.1358v3 [math.NT]). We also provide a zero-density theorem for the product, which follows from Soundararajan's theorem for moments of the Riemann…

A non-trivial symbolic machinery is presented that can rephrase algorithmically a finite set of nested hypergeometric products in appropriately designed difference rings. As a consequence, one obtains an alternative representation in terms…