Related papers: A Remark on the Higher Capelli Identities

A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.

We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.

We improve the previuosly known bound for some vertex Folkman numbers.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…

We consider remarkable central elements of the universal enveloping algebra of the general linear algebra which we call quantum immanants. We express them in terms of generators $E_{ij}$ and as differential operators on the space of…

By using the notion of a quantum double we introduce analogs of partial derivatives on a Reflection Equation algebra, associated with a Hecke symmetry of GL(N) type. We construct the matrix L=MD, where M is the generating matrix of the…

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

Binomial versions of the Andrews-Gordon-Bressoud identities are given.

We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.

Some question about representations of $p$-adic groups are discussed.

Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a…

We show that, up to multiplication by a factor $\frac{1}{(cq;q)_{\infty}}$, the weighted words version of Capparelli's identity is a particular case of the weighted words version of Primc's identity. We prove this first using recurrences,…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

We extend the lift application for automorphic induction defined by an identity of characters to all elliptic representations.

Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.

We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the $q$-Fibonacci polynomials appearing in Schur's work. The proofs of most of…

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…