A note on p-adic Carlitz's q-Bernoulli numbers

Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers

Let p be a fixed prime number. Throughout this paper, the symbols Z,Zp,Qp,C, and Cp will denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. Let vp be the normalized exponential valuation of Cp with |p|...

p-Adic Measures and Bernoulli Numbers

A NOTE ON p-ADIC q-INTEGRAL ASSOCIATED WITH q-EULER NUMBERS

Abstract. We show that q-Euler numbers can be represented as an integral by the q-analogue of the ordinary p-adic fermionic measure, whence we give an answer to the question of readers to ask us for the fermionic p-adic q-integral on Zp. Sometimes several readers give the nonsense comments to us. But we do not write their names in this paper. I would like to tell the readers that papers are dif...

A note on q-Bernoulli numbers and polynomials

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

A note on q-Bernoulli numbers and polynomials

Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...