Related papers: Unit circle elliptic beta integrals
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
This paper gives a detailed derivation of the surface of a tri-axial ellipsoid. The general result is in terms of the elliptic integrals of the first and second kind. It is in checked for all special cases included and the corresponding…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
The hadronic decays eta -> pi pi pi, eta-prime -> pi pi pi and eta-prime -> eta pi pi are investigated within a U(3) chiral unitary approach. Final state interactions are included by deriving the effective s-wave potentials for meson meson…
Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
A consistent treatment of intrinsic and collective coordinates is applied to the calculation of matrix elements describing nuclear double beta decay transitions. The method, which was developed for the case of nuclear rotations, is adapted…
We find explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper we proved that such formulas should exist. We give applications to the…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by \begin{gather*} \begin{cases} -\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla…
We discuss the basic properties of various versions of two variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the…
Let $X$ be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each $X$ we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of…
In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some properties of the degenerate Laplace transform and degenerate gamma function. From our investigation, we derive some interesting…
It is conjectured that a class of n-fold integral transformations {I(alpha)|alpha in {C}} forms a mutually commutative family, namely, we have I(alpha) I(beta)=I(beta) I(alpha) for all alpha, beta in {C}. The commutativity of I(alpha) for…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal power series ring. In order to do this, we use an integral…
We consider a univariate beta integral composed from general modular quantum dilogarithm functions and prove its exact evaluation formula. It represents the partition function of a particular $3d$ supersymmetric field theory on the general…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…