Related papers: On the evaluation of some Selberg-like integrals

In this article we consider the elliptic Selberg integral, which is a BC_n symmetric multivariate extension of the elliptic beta integral. We categorize the limits that are obtained as p->0, for given behavior of the parameters as p->0.…

The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…

The goal of the course was a review of results mainly due to M. Olbrich and the first author. We consider a discrete cocompact subgroup $\Gamma$ of a semisimple Lie group $G$. We relate the group cohomology of $\Gamma$ with coefficients in…

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test…

We consider a certain sequence of flat vector bundles on a compact locally symmetric orbifold, and we evaluate explicitly the associated asymptotic Ray-Singer real analytic torsion. The basic idea is to computing the heat trace via…

In this paper, new asymptotic formulas for sums over zeros of functions from the Selberg class are obtained. These results continue the investigations of Murty $\&$ Perelli \cite{12}, of Murty $\&$ Zaharescu \cite{13}, of Kamiya $\&$ Suzuki…

We consider some new limits for the elliptic hypergeometric integrals on root systems. After the degeneration of elliptic beta integrals of type I and type II for root systems $A_n$ and $C_n$ to the hyperbolic hypergeometric integrals, we…

Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a…

Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by R.J.Evans in 1981 and, following an elegant idea of G.W.Anderson in 1991 they were…

Using an extension of the well-known evaluation symmetry, a new Cauchy-type identity for Macdonald polynomials is proved. After taking the classical limit this yields a new sl_3 generalisation of the famous Selberg integral. Closely related…

Let $G$ be a semisimple Lie group with discrete series. We use maps $K_0(C^*_rG)\to \mathbb{C}$ defined by orbital integrals to recover group theoretic information about $G$, including information contained in $K$-theory classes not…

Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…

We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma…

A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to $A_n$ type root system both in the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a…

In this paper, we first establish explicit evaluations of six classes of hyperbolic sums by special values of the Gamma function by using the tools of the Fourier series expansions and the Maclaurin series expansions of a few Jacobi…

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…

In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals,…

We study elements of the spectral theory of compact hyperbolic orbifolds $\Gamma \backslash \mathbb{H}^{n}$. We establish a version of the Selberg trace formula for non-unitary representations of $\Gamma$ and prove that the associated…

In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a…

We consider a reductive dual pair (G, G') in the stable range with G' the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K'_C-orbits, where K' is a maximal compact subgroup of G' and we describe the…