相关论文: A q-analogue of Wolstenholme's harmonic series con…

With the help of El Bachraoui's lemma, the creative microscoping method, and a new form of the Chinese remainder theorem for coprime polynomials, we prove a $q$-supercongruence for double series and a $q$-supercongruence for triple series…

We present a relative form of the Toponogov comparison theorem.

In this paper we give two results on the logarithmic cotangent complex: we construct a logarithmic analogues to the complex of Lichtenbaum and Schlessinger and to Quillen's fundamental spectral sequence.

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

We prove a q-analogue of the formula $ \sum_{1\le k\le n} \binom nk(-1)^{k-1}\sum_{1\le i_1\le i_2\le... \le i_m=k}\frac1{i_1i_2... i_m} = \sum_{1\le k\le n}\frac{1}{k^m} $ by inverting a formula due to Dilcher.

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…

We prove a stability version of the Pr\'ekopa-Leindler inequality.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

In this paper, we derive a recurrence relation of anti-forcing polynomial for catacondensed hexagonal systems.

In this paper, by constructing some identities, we prove some $q$-analogues of some congruences. For example, for any odd integer $n>1$, we show that \begin{gather*} \sum_{k=0}^{n-1} \frac{(q^{-1};q^2)_k}{(q;q)_k} q^k \equiv (-1)^{(n+1)/2}…

In this paper we present many congruences for several Ap\'ery-like sequences.

We prove that cyclotomic Yokonuma--Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras. The quiver…

The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that…

The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even, $t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$, where $a$ and $b$ are…

A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…

We survey the classical results of the Dirichlet Approximation Theorem.

Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.