M. Papikian

Non-Archimedean Poincar\'e series and geodesics on the Bruhat-Tits tree

Adapting a construction of Kurihara in the setting of Drinfeld modular forms, we define Poincar\'e series on the Drinfeld half-plane $\Omega$. These series are built from products of meromorphic $1$-forms that are naturally associated to geodesics on the Bruhat-Tits tree. We establish convergence under a finiteness con...