Related papers: Recursion Relation of Hyperelliptic Psi-Functions …
A double covering of the proper orthochronous Lorentz group is understood as a complexification of the special unimodular group of second order (a double covering of the 3-dimensional rotation group). In virtue of such an interpretation the…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
In this paper we combine the fractional $\psi-$hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel-Pompeiu type formula related to a fractional $\psi-$Fueter…
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.
We show that the Eynard-Orantin topological recursion, in conjunction with simple auxiliary equations, can be used to calculate all correlation functions of supereigenvalue models.
In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for…
We calculate the genus 2 correlation functions of two-dimensional topological gravity, in a background with two primary fields, using the genus 2 topological recursion relations.
In recent years, there has been significant progress in the theory of orthogonal polynomials on algebraic curves, particularly on genus 1 surfaces. In this paper, we focus on elliptic orthogonal polynomials and establish several of their…
We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions,…
The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. Here a set A is called pdominant iff there is a partial A-recursive function {\psi} such that for every partial recursive function…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we…
In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev-Petviashvili equations KP-I and KP-II are obtained. The…
We introduce an elliptic extension of Clausen-type functions based on a unified recursive framework. Starting from the polylogarithmic master function, we construct a pair of circular functions whose real and imaginary parts correspond to…
We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $\sigma$-function. These functions are related to weight 2 $\theta$-functions in the same fashion as…
We obtain extensions of the Poincar\'e and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power…
This paper studies three different ways to assign weights to the lattice points of a convex polytope and discusses the algebraic and combinatorial properties of the resulting weighted Ehrhart functions and their generating functions and…
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or $\mathbb R^3$) with values in $\mathbb H$. This theory is centered around the concept of $\psi-$hyperholomorphic functions i.e.,…
The recursion relations are derived for multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level.…