Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Geodesics on the Bruhat-Tits tree and Poincaré series
Milan Berger-Guesneau (Pennsylvania State University)
Abstract
In their 1994 paper "On p-adic Poincaré series and Shimura curves", Kurihara defined a class of p-adic modular forms called Poincaré series. Using an ingenious combinatorial argument, they proved that these Poincaré series generate the whole space of modular forms. In this talk, I will explain how to adapt the proof for subgroups of GL2(Fq[T]). Poincaré series depends on parameters chosen in the boundary of the Bruhat-Tits tree; these parameters thus define geodesics in the tree. We will see that the valuation of Poincaré series depends on the way in which these geodesics intersect.
Organizer: Fu-Tsun Wei (NTHU)
