Construction of a Dimension Two Rank One Drinfeld Module

Consider Fr[t] where r = pm for some prime p and m in the natural numbers. Let f(t) be an irreducible square-free polynomial with even degree in Fr[t] so that the leading coeffcient is not a square mod Fr. Let A = L = Fr[t][\sqrt{f(t)}]. We will examine the basic set-up required for a dimension two rank one Drinfeld module over L along with an explanation of our choice of f(t). In addition we will show the construction for the exponential function