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 study the identities of symmetry for the generalized higher-order q-Euler polynomials in three variable under symmetry group S 3 which are derived from the...

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. The p-adic absolute value in Cp is normalized so that |p|p = 1 p . When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C or a p-adic numbe...

*Correspondence: [email protected] 3Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Republic of Korea Full list of author information is available at the end of the article Abstract We use the p-adic q-integral and group action to count the number of the generating functions of modified q-Euler polynomials in a prescribed set. Some generating function yield...

Cangul-Ozden-Simsek[1] constructed the q-Genocchi numbers of high order using a fermionic p-adic integral on Zp, and gave Witt’s formula and the interpolation functions of these numbers. In this paper, we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers of Cangul-Ozden-Simsek. We define q-extensions of w-Euler numbers and polynomials, and w-Genocchi numbers ...

New approach to p-adic and adelic strings, which takes into account that not only world sheet but also Minkowski space-time and string momenta can be p-adic and adelic, is formulated. p-Adic and adelic string amplitudes are considered within Feynman’s path integral formalism. The adelic Veneziano amplitude is calculated. Some discreteness of string momenta is obtained. Also, adelic coupling con...

Part II. p-adic methods §3. Considerations on the differential case §4. Introduction to p-adic q-difference modules 4.1. p-adic estimates of q-binomials 4.2. The Gauss norm and the invariant χv(M) 4.3. q-analogue of the Dwork-Frobenius theorem §5. p-adic criteria for unipotent reduction 5.1. q-difference modules having unipotent reduction modulo ̟v 5.2. q-difference modules having unipotent redu...

The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the...

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics. 1. It is well known that dynamical evolution of any one-dimensional quantum-mechanical system, described by a wave function Ψ(x, t), is given by Ψ(x ′′ , t...

Araci et al. introduced a $$p$$ -adic $$(\rho,q)$$ -analogue of the Haar distribution. By means distribution, they constructed -Volkenborn integral. In this paper, by virtue Mahler expansion continuous functions, author gives Radon-Nikodym theorem with respect to -distribution on $$\Bbb Z_p$$ .