p-adic Number Theory

I studied chapters 1, 2, and 4 from Neal Koblitz’s “p‐adic Numbers, p‐adic Analysis and Zeta functions”. I read the following papers as part of the project: “The derivative of p‐adic Dirichlet series at s=0” [Stark’s Conjectures: Recent Work and New Directions, (2004)] and “On the p‐adic series involving the infinite sum n^{k}. n! [CRM Lecture Notes, 2004]. I could generalize the results of the second paper for arithmetic progressions.