This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we investigate some symmetric properties of p-adic q-integral on Z p. A question was asked in [10] as to finding formulae of symmetries for the generalized Ca...

and Applied Analysis 3 The purpose of this paper is to derive a new concept of higher-order q-Bernoulli numbers and polynomials with weight α from the fermionic p-adic q-integral on Zp. Finally, we present a systemic study of some families of higher-order q-Bernoulli numbers and polynomials with weight α. 2. Higher Order q-Bernoulli Numbers with Weight α Let β ∈ Z and α ∈ N in this paper. For k...

Abstract In a recent work of Anderson and Hu, the authors constructed measure that was p-adic q-adic doubling, for any primes p q, yet not doubling. This relied heavily on developed number theory framework. Here we develop this framework further, which yields is m-adic n-adic doubling coprime $m,n$, Additionally, show several new applications to intersection weight function classes.

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

where ((x)) = x − [x]G − 1 2 , if x / ∈ Z, ((x)) = 0, x ∈ Z, where [x]G is the largest integer ≤ x cf. ([1], [5], [9], [11], [12], [13]). In this paper, Zp, Qp, Cp, C and Z, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, the p-adic completion of the algebraic closure of Qp normalized by |p|p = p −1, and the complex field and integer numbers. Let q be an ...

Let p be a fixed prime number. Throughout this paper, p, p , and p will denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of the algebraic closure of p , respectively. Let be the set of natural numbers, and let ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Let q be regarded as either a complex number q ∈ or a p-adic n...

Abstract : The object of this paper is to give several properties and applications of the multiple p-adic q-L-function of two variables L (r) p,q (s, z, χ). The explicit formulas relating higher order qBernoulli polynomials, which involve sums of products of higher order q-zeta function and higher order Dirichlet q-L-function are given. The value of higher order Dirichlet p-adic q-L-function fo...

The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral Teichmüller character representations Bernoulli polynomials, we give reciprocity law these These sums their generalized some classical Dedekind law. It be noted that laws, a fine study existing symmetry relations between finite sums, considered in our study, symmetries through permutations...

Let p be a fixed odd prime. 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) = p and let q be regarded as either a complex number q ∈ C or a p-adic number q...