P-Adic hurwitz-lerch L-function

This work consists of two parts. We first reconstruct the p-adic Hurwitz-Lerch L-function by employing partial zeta functions. This construction is different from that of Morita's. Using this function we investigate divisibility properties and Kummer type congruences for generalized Apostol-Bernoulli polynomials, which occur as the values of Hurwitz-Lerch L-function at negative integers. In the second part we define Barnes' type Hurwitz-Lerch zeta function by employing the residue theorem and complex integration. We consider the values of this function at negative integers, which are called multiple Apostol-Bernoulli polynomials of order N, and discuss some of their properties. Using these polynomials we construct a p-adic analogue of Barnes'type Hurwitz-Lerch zeta function.