q-Bernoulli Numbers and Polynomials Associated with Multiple q-Zeta Functions and Basic L-series

By using q-Volkenborn integration and uniform differentiable on Z%ₚ, we construct p-adic q-zeta functions. These functions interpolate the q-Bernoulli numbers and polynomials. The value of p-adic q-zeta functions at negative integers are given explicitly. We also define new generating functions of q-Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of some basic (or q-) L% -series. These generating functions also interpolate Barnes' type Changhee $% q $-Bernoulli numbers with attached to Dirichlet character as well. By applying Mellin transformation, we obtain relations between Barnes' type q% -zeta function and new Barnes' type Changhee q-Bernolli numbers. Furthermore, we construct the Dirichlet type Changhee (or q-) L% -functions.