The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to χ from the properties of the p-adic invariant integral. We give some interesting identities for the power sums and the generalized twisted Bernoulli numbers and polynomials of higher order using the symmetric properties of the p-adic invariant integral. 20...

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representat...

To Dong-Sik Kim on his 62nd birthday We try to generalize an explicit construction for an orthonormal system of eigen-functions of the Vladimirov operator on L 2 (Q n p) which was originally given by Vladimirov (1988). Also the multiwavelet analysis can be considered as the p-adic spectral analysis in L 2 (Q n p), using in part the recent work of Kozyrev (2002). denote the ring of integers, the...

Throughout this paper, we always make use of the following notations: C denotes the set of complex numbers, Zp denotes the ring of p-adic rational integers, Qp denotes the field of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. When one talks of q-extension, q is considered in man...

Let p be a fixed prime number. Throughout this paper Zp,Qp,C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks of q-extension, q is variously considered as an indeterminate,...

Abstract. The purpose of this paper is to construct of λ-Euler numbers and polynomials by using fermionic expression of p-adic q-integral at q = −1. From these λ-Euler polynomials, we derive the harmonic sums of higher order. Finally, we investigate several interesting properties and relationships involving the classical as well as the generalized Euler numbers and polynomials. As an applicatio...

The implementation of the concept «smart city» has required, in particular, development and efficient use new mathematical methods approaches enabling data hypercube analysis to be made efficiently constructively, transfer processes initiated, etc.

Let p be a fixed odd prime number. Throughout this paper Z, Q, Zp, Qp and Cp will respectively denote the ring of rational integers, the field of rational numbers, the ring p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp such that |p|p = p−vp(p) = p−1. If q ∈ Cp, we normally as...