相关论文: On p-adic q-l-functions and sums of powers

In the paper, using the extended fermionic $p$-adic integral on $\mathbb{Z}_p$, the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and…

In this paper we have discussed convergence of power series both in p-adic norm as well as real norm. We have investigated rational summability of power series with respect to both p-adic norm and real norm under certain conditions. Then we…

Recently, the two variable $q$-$L$-functions which interpolate the generalized $q$-Bernoulli polynomials associated with $\chi$ are introduced and studied, cf. [2]. In this paper, we construct multiple Dirichlet's $q$-$L$-function which…

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$. By applying their generating functions,…

The fundamental aim of this paper is to describe q-Analogue of p-adic log gamma functions with weight alpha and beta. Moreover, we give relationship between p-adic q-log gamma funtions with weight ({\alpha}, {\beta}) and q-extension of…

Let $E$ be a rational elliptic curve and let $p$ be an odd prime of additive reduction. Let $K$ be an imaginary quadratic field and fix a positive integer $c$ prime to the conductor of $E$. The main goal of the present article is to define…

In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…

In this paper, using p-adic integration with values in spaces of modular forms, we construct the p-adic analogue of Weil's elliptic functions according to Eisenstein in the book "Elliptic functions according to Eisenstein and and…

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…

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…

Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that…

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.

By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions…

In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…

The purpose of this paper is to study the special values of the standard $L$-functions for quaternionic modular forms using the doubling method. We obtain an integral representation for the $L$-function twisted by a character and construct…

In this paper we study the properties of an algorithm for generating continued fractions in the field of p-adic numbers $\mathbb{Q}_p$. First of all, we obtain an analogue of the Galois' Theorem for classical continued fractions. Then, we…

We construct $p$-adic multiple $L$-functions in several variables, which are generalizations of the classical Kubota-Leopoldt $p$-adic $L$-functions, by using a specific $p$-adic measure. Our construction is from the $p$-adic analytic side…

We consider formal power series defined through the functional q-equation of the q-Lagrange inversion. Under some assumptions, we obtain the asymptotic behavior of the coefficients of these power series. As a by-product, we show that, via…

For \psi a nontrivial additive character on the finite field F_q, the map t \mapsto \sum_{x \in F_q} \psi(f(x)+tx) is the Fourier transform of the map t \mapsto \psi(f(t))$. As is well-known, this has a cohomological interpretation,…

The aim of this note is to provoke discussion concerning arithmetic properties of function $p_{d}(n)$ counting partitions of an positive integer $n$ into $d$-th powers, where $d\geq 2$. Besides results concerning the asymptotic behavior of…