Related papers: Representing ($q$--)hypergeometric products and mi…

Two methods can be used to calculate explicitly the Killing form on the Lie algebras. The first one is a direct calculation of the traces of the generators in a matrix representation of the algebra, and the second one is the usage of the…

By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.

An unpublished identity of Gosper restates a hypergeometric identity for odd zeta values in terms of an infinite product of matrices. We show that this correspondence runs much deeper, and show that many examples of WZ-accelerated series…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

Let $\F_q$ be a finite field of order $q$ and $P$ be a polynomial in $\F_q[x_1, x_2]$. For a set $A \subset \F_q$, define $P(A):=\{P(x_1, x_2) | x_i \in A \}$. Using certain constructions of expanders, we characterize all polynomials $P$…

We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over…

A product system E over a semigroup P is a family of Hilbert spaces {E_s:s\in P} together with multiplications E_s \times E_t\to E_{st}. We view E as a unitary- valued cocycle on P, and consider twisted crossed products A \times_{\beta,E} P…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…

This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible…

We consider products of $\psi$ classes and products of $\omega$ classes on $\overline{M}_{0,n+3}$. For each product, we construct a flat family of subschemes of $\overline{M}_{0,n+3}$ whose general fiber is a complete intersection…

We prove that the module categories of Noether algebras (i.e., algebras module finite over a noetherian center) and affine noetherian PI algebras over a field enjoy the following product property: Whenever a direct product $\prod_{n \in…

We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.

This survey article is devoted to the notions of purity, algebraic and $\Sigma$-algebraic compactness, direct sum decompositions, and representation type in the category of modules over a ring. It begins with basic definitions, a brief…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…

We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…

We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions…