Related papers: Wilson Theorems for Double-, Hyper-, Sub- and Supe…
We introduce a new generalization of Euler's $\varphi$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do…
This note is a short introduction to the Julia-Wolff-Carath\'eodory theorem, and its generalizations in several complex variables, up to very recent results for infinitesimal generators of semigroups.
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed.
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
We prove a generalization of the digital binomial theorem by constructing a one-parameter subgroup of generalized Sierpinski matrices. In addition, we derive new formulas for the coefficients of Prouhet-Thue-Morse polynomials and describe…
In this short note we give counterexamples to several results related to extension theorems published recently.
A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously known addition formulas for $q$-Legendre…
We present a slightly more general version of Boole's additive formula for factorials as a simple consequence of Lagrange's Interpolating Polynomial theorem.
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$…
We generalize the standard product integral formalism to incorporate Grassmann valued matrices and show that the resulting supersymmetric product integrals provide a natural framework for describing supersymmetric Wilson Lines and Wilson…
Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of…
New and old results on closed polynomials, i.e., such polynomials f in K[x_1,...,x_n] that the subalgebra K[f] is integrally closed in K[x_1,...,x_n], are collected. Using some properties of closed polynomials we prove the following…
\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…
Many Texo's have been corrected and a reference added.
This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent…