Adelic Voronoi summation and subconvexity for GL(2) L-functions in the depth aspect

In this paper, we establish a very flexible and explicit Voronoi summation formula. This is then used to prove an almost Weyl strength subconvexity result for automorphic L-functions of degree two in the depth aspect. That is, looking at twists by characters of prime power conductor. This is the natural p-adic analogue to the well-studied t-aspect.