p-Adic automorphic distributions

To an automorphic representation there is an attached automorphic distribution; these automorphic distributions were used by Miller and Schmid to construct generalized Voronoi summation formulas for GLn(Z)-automorphic representations of GLn(R). The goal of this thesis is to set the framework of automorphic distributions for GL2(A). The methods of Miller and Schmid work well for subrepresentations of principal series; however, the representation theory of GL2(Q) contains supercuspidal representations, for which their methods do not apply. Supercuspidal representations are handled by a choice of a suitable model, which comes from theta correspondence with the Weil representation. We realize the automorphic distribution as a sum of products of local Whittaker functionals, which are explicitly computable in models.