The Artin Hasse Exponential and the p-adics

<p>In 1928, the Artin-Hasse Exponential E(x) was created and it’s considered an analogue of the exponential function that comes from infinite products. It also has applications in formal group schemes and is studied in the p-adic number system. In this paper, fundamental results about the field of the p-adic rationals, Qp, like completion, are proven while smaller propositions are left to the reader. The integrality of E(x) is shown using Dwork’s Lemma and extensions of the Artin Hasse exponential are further discussed.</p>