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

A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.

We introduce signed q-analogs of Tornheim's double series, and evaluate them in terms of double q-Euler sums. As a consequence, we provide explicit evaluations of signed and unsigned Tornheim double series, and correct some mistakes in the…

We introduce a $q$-analog of the polyanalytic Bargmann transform on $\mathbb{C}$.

We investigate a variation of $q$-Wolstenholme's theorem, which extends the $q$-analogue of Wolstenholme's theorem due to Shi and Pan [Amer. Math. Monthly 114 (2007), 529--531]. The proof makes use of the Ramanujan sum and higher order…

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…

We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that \[ \binom{a p}{b p} \equiv \binom{a}{b} \] modulo $p^3$ for primes $p\ge5$. This congruence subsumes and builds on earlier congruences by Babbage,…

We propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete…

Orthogonal q-polynomials associated with q-Laguerre-Hahn form will be studied as a generalization of the q-semiclassical forms via a suitable q-difference equation. The concept of class and a criterion to determinate it will be given. The…

In this article we study some interesting properties of the $q$-Analog singular homology, which is a generalization of the usual singular homology, suitably adapted to the context of $N$-complex and amplitude homology \cite{kapranov}. We…

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation…

We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

We prove q-analogues of two Ramanujan-type series for $1/\pi$ from $q$-analogues of ordinary WZ pairs.

In this article we give a proof of a q-analogue of the celebrated four functions theorem. This analogue was conjectured by Bjorner and includes as special cases both the four functions theorem and also Bjorner's q-analogue of the FKG…

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

In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.

Motivated by the recent research of congruences and $q$-congruences, we provide two different $q$-analogues of the (G.2) supercongruence of Van Hamme through the `creative microscoping' method, which was devised by Guo and Zudilin. It is a…

We discuss an arithmetic approach to some congruence properties of Siegel theta series of even positive definite unimodular quadratic forms.

We construct a subalgebra of the Hecke algebra of type A. This is a generalization of the group algebra of the alternating groups. All the equivalent classes of irreducible representations of the subalgebra and the q-analogue of the…

In this paper, we study the Lehmer's type congruences for lacunary harmonic sums.