Related papers: Rarefied elliptic hypergeometric functions
We study the integrable system of first order differential equations $\omega_i(v)'=\alpha_i\,\prod_{j\neq i}\omega_j(v)$, $(1\!\leq i, j\leq\! N)$ as an initial value problem, with real coefficients $\alpha_i$ and initial conditions…
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental…
The notion of integral Bailey pairs is introduced. Using the single variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric integrals. Two particular sequences of identities are…
In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in $\mathbb{R}^n$ and for the corresponding…
This article surveys results on graded algebras and their Hilbert series. We give simple constructions of finitely generated graded associative algebras $R$ with Hilbert series $H(R,t)$ very close to an arbitrary power series $a(t)$ with…
We compute the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function…
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…
We consider integrals that generalize both the Mellin transforms of rational functions of the form 1/f and the classical Euler integrals. The domains of integration of our so-called Euler--Mellin integrals are naturally related to the…
Recently, Kajihara gave a Bailey-type transformation relating basic hypergeometric series on the root system An, with different dimensions n. We give, with a new, elementary, proof, an elliptic analogue of this transformation. We also…
Orbifold elliptic genus and elliptic genus of singular varieties are introduced and relation between them is studied. Elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of…
Classical hypergeometric functions are well-known to play an important role in arithmetic algebraic geometry. These functions offer solutions to ordinary differential equations, and special cases of such solutions are periods of…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
Recently we have found an analytic integration formula that describes the dependence of the luminosity distance on the redshift for the flat cosmological model with a non-zero cosmological constant. The purpose of this article is to search…
We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields…
In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will…
A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are…
We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed…
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…
We study functions of an elliptic parameter, which are defined as iterated integrals of elliptic functions. We establish their relation with the "elliptic associators" of our previous work, by means of a functional realization of Lie…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…