Pseudodifferential operators associated to linear ordinary differential equations

Abstract

We investigate connections between pseudodifferential operators and linear ordinary differential equations via their respective links to automorphic forms. We also introduce Hecke operators on the space of pseudodifferential operators as well as on the space of certain meromorphic functions associated to ordinary differential equations and prove that the actions of those Hecke operators are compatible with the correspondence between pseudodifferential operators and linear ordinary differential equations.