On Carlitz's Type q-Euler Numbers Associated with the Fermionic P-Adic Integral on Z(p)

Abstract

We consider the following problem in the paper of Kim et al. (2010): "Find Witt's formula for Carlitz's type q-Euler numbers." We give Witt's formula for Carlitz's type q-Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function l(p,q) (s, chi) for Dirichlet's character chi, with the property that lp,q (-n, chi) - E-n,E-chi n,E-q - chi(n)(p)[p](q)'' E-n,E-chi n,E-qp for n = 0, 1, ... using the fermionic p-adic integral on Z(p).