q-BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH MULTIPLE q-ZETA FUNCTIONS AND BASIC L-SERIES

By using q-Volkenborn integration and uniform differentiable on Zp, we construct p-adic q-zeta functions. These functions interpolate the qBernoulli 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.