Hurwitz class numbers in the theory of automorphic forms, and an extension to totally real number fields

Abstract

Hurwitz class numbers occur in various places in the theory of classical modular and Jacobi forms.Recently, in joint work with N-P Skoruppa, we found an extension of this theory to (totally real)number fields. In this talk we explain the context for these considerations, introduce the pendantsof Hurwitz class numbers in totally real number fields and the appearance of these new numbers inthe theory of Jacobi forms over number fields.