The present paper deals with the various q-Genocchi numbers and polynomials. We define a new type ofmultiple generalized q-Genocchi numbers and polynomials withweight α andweakweight β by applying the method of p-adic q-integral. We will find a link between their numbers and polynomials with weight α and weak weight β. Also we will obtain the interesting properties of their numbers and polynomi...

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interest...

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 the algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p −νp(p) = 1 p . When one talks of q-extension, q is variously considered as an indeter...

Let p be a fixed 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, cf.[1, 4, 6, 10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. When one talks of q-extension, q is variously considered as an...

Vogan has conjectured that a family of cohomologically induced modules exhaust the unitary dual of U(p, q) for certain kinds of integral infinitesimal characters. In this expository note (which is substantially a transcript of a talk given at the 1997 Seattle conference on the representation theory of real and p-adic groups) we recall the definition of the relevant modules, describe an approach...

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...

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)

Let p be a fixed odd prime. Throughout this paper Zp,Qp,C, andCp, 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 N be the set of natural numbers and Z N ∪ {0}. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1 see 1–14 . When one speaks of ...