Related papers: Several integrals of quaternionic field on hyperbo…
Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…
With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil-Petersson form. Mirzakhani proved that Weil-Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers…
In this paper we give the characterization of Fuchsian groups acting on quaternionic hyperbolic 2-space.
By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit…
We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the…
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
We construct new examples of embedded, complete minimal hypersurfaces in quaternionc hyperbolic space and also some minimal foliations. We introduce fans an construct analytic deformations of bisectors.
We derive an explicit lower bound on the radius of a ball embedded in a quaternionic hyperbolic manifold.
We calculate the modulus of curve families inside a hyperbolic quadrilateral and a hyperbolic annulus.
In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…
The matrix integral has many applications in diverse fields. This review article begins by presenting detailed key background knowledge about matrix integral. Then the volumes of orthogonal groups and unitary groups are computed,…
We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension $2$.…
The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gauss…
We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.
The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism…
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.