Related papers: Dirichlet's type of twisted Eulerian polynomials i…
In this paper, we investigate some new symmetric identities for the q-Euler polynomials under the symmetric group of degree n which are derived from fermionic p-adic q-integrals on Zp.
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Zp. By using these properties, we give some interesting identities related to higher- order q-Bernoulli…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
Hamiltonians ${\cal H}^{a}_k$ of new integrable systems associated with the integer rays $(1,a)$ (commutative subalgebras) of Ding-Iohara-Miki (DIM) algebra in the $N$-body representation are closely related to commuting twisted Cherednik…
Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with…
We define some generalizations of the classical descent and inversion statistics on signed permutations that arise from the work of Sack and Ulfarsson [20] and called after width-k descents and width-k inversionsof type A in Davis's work…
Let $L/F$ be a quadratic extension of totally real number fields. For any prime $p$ unramified in $L$, we construct a $p$-adic $L$-function interpolating the central values of the twisted triple product $L$-functions attached to a…
In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials
The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating…
In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…
Suppose that $\omega_1,\ldots,\omega_N$ are positive real numbers and $x$ is a complex number with positive real part. The multiple Barnes-Euler zeta function $\zeta_{E,N}(s,x;\bar\omega)$ with parameter vector…
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.
Recently, Boole polynomials have been studied by Kim and Kim over the p-adic number field. In this paper, we consider a q-extension of Boole polynomials by using the fermionic p-adic integrals on Zp and give some new identities related to…
Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on…
Let $\mathcal{A}$ be a Weyl arrangement. We introduce and study the notion of $\mathcal{A}$-Eulerian polynomial producing an Eulerian-like polynomial for any subarrangement of $\mathcal{A}$. This polynomial together with shift operator…
The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. we unify all forms of q-exponential functions by one more parameter. we…
We find a combinatorial interpretation of Shareshian and Wachs' $q$-binomial-Eulerian polynomials, which leads to an alternative proof of their $q$-$\gamma$-positivity using group actions. Motivated by the sign-balance identity of…
In this article, we study $p$-adic torus periods for certain $p$-adic valued functions on Shimura curves coming from classical origin. We prove a $p$-adic Waldspurger formula for these periods, generalizing the recent work of Bertolini,…