Hilbert Spaces of Entire Functions and Automorphic L-Functions

JOINT PU/IAS NUMBER THEORY SEMINAR
Topic:Hilbert Spaces of Entire Functions and Automorphic L-Functions
Speaker:J. Lagarias
Affiliation:University of Michigan
Date:Thursday, February 28
Time/Room:4:30pm - 5:30pm/S-101

We review the de Branges theory of Hilbert spaces of entire functions. This theory gives a canonical form for a class of operators as a multiplication operator together with a generalized Fourier transform taking such an operator to a generalized differential operator. We discuss its relation to other theories of canonical forms for certain non-self adjoint operators, including “model spaces” and Lax-Phillips scattering theory. We present examples, including de Branges spaces associated to automorphic L-functions, and discuss how the Riemann hypothesis may be encoded in this framework.