Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms

Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane I to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in I according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincare summation process, which consists in building au