# Meeting Details

Title: "Zeta Functions of Complexes from PGSP$4$)" Ph.D. Thesis Defense Yang Fang, Adviser: Wen-Ching Winnie Li, Penn State Adviser: W. Li In this thesis we study the zeta functions arising from PGSp(4) over a nonarchimedean local field. In this case, the complexes have dimension two, like PGL(3). However, the vertices are distinguished as special and nonspecial vertices, unlike the case of PGL(3). We define the (edge) zeta function as the counting function of the number of tailless closed geodesics of all type-one or type-two edges, which has a closed form expression in terms of parahoric Hecke operators. The main result shows that the zeta function satisfies a zeta identity involving the Euler characteristic of the complex, the characteristic polynomial of the recurrence relations of the Hecke algebra, the Iwahori-Hecke operator and the number of special and nonspecial vertices. Moreover, we study the operators on nonspecial vertices.