Related papers: A q-analogue of Wolstenholme's harmonic series con…

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.

In the paper, we generalize some congruences of Lehmer for general composite numbers.

Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.

A difference q-analogue of the dressing chain is discussed in this paper.

In this paper, the divisibility property of the type 2 $(p, q)$-analogue of the $r$-Whitney numbers of the second kind is established. More precisely, a congruence relation modulo $pq$ for this $(p,q)$-analogue is derived.

Let ${\mathcal C}_n$ be the set of all permutation cycles of length $n$ over $\{1,2,\ldots,n\}$. Let $${\mathfrak f}_n(q):=\sum_{\sigma\in{\mathcal C}_{n+1}}q^{{\mathrm maj}\,\sigma} $$ be a $q$-analogue of the factorial $n!$, where…

We prove an analogue of the prime number theorem for finite fields.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

Some q-analogues of classical integral transforms have recently been investigated by many authors in diverse citations. The q-analogues of the Natural transform are not known nor used. In the present paper, we are concerned with definitions…

We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.

We prove that the Lalescu sequence is monotonically decreasing.

A $\tphin$ contiguous relation is used to derive contiguous relations for a very-well-poised $\ephis$. These in turn yield solutions to the associated $q$-Askey-Wilson polynomial recurrence relation, expressions for the associated continued…

A tutorial introduction is given to q-special functions and to q-analogues of the classical orthogonal polynomials, up to the level of Askey-Wilson polynomials.

In this note we show that various natural q-analogues of the Catalan numbers can be obtained in a uniform way. Furthermore we compute their Hankel determinants.

The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.

In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference…

Variants of the q-hypergeometric equation were introduced in our previous paper with Hatano. In this paper, we consider degenerations of the variant of the q-hypergeometric equation, which is a q-analogue of confluence of singularities in…

We give a formula for a $q$-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms. In the limit as $q\to 1$, this formula reduces to an identity equivalent to the Sakugawa-Seki identities. We also give a formula…

A symplectic realization and some symmetries of a Rikitake type system are presented.