Dirichlet Series Expansions of p-adic L-functions

We study p-adic L-functions Lp(s, χ) for Dirichlet characters χ. We show that Lp(s, χ) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of χ. The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for c= 2 , where we obtain a Dirichlet series expansion that is similar to the complex case.