Interpolating the Riemann Zeta Function in the p-adics

In this thesis, we develop the Kubota-Leopoldt Riemann zeta function in the p-adic integers. We follow Neil Koblitz\u27s interpolation of Riemann zeta, using Bernoulli measures and p-adic integrals. The underlying goal is to better understand p-adic expansions and computations. We finish by connecting the Riemann zeta function to L-functions and their p-adic interpolations