Number Theory Seminar: Julia Gordon (UBC)

I will talk about a class of functions on local fields that can be defined by means of logic (the so-called constructible exponential functions). These functions are in a sense built from charactersitic functions of balls, and additive characters of the field. It turns out that they have unexpectedly simple "integration theory". It also turns out that Harish-Chandra characters of representations of p-adic groups near the identity element belong to this class of functions. This allows to transfer Harish-Chandra's theorem about local integrability of characters that was known in general only for local fields of characteristic zero, to large positive characteristic. All of the notions mentioned in this abstract will be defined in the talk.