On the characteristic p valued measure associated to Drinfeld discriminant

In this paper, after reviewing known results on functions over Bruhat–Tits trees and the theory of characteristic p valued modular forms, we present some structure of the tempered distributions on the projective space P1(k∞) over a complete function field k∞ of characteristic p, and calculate the characteristic p valued measure associated to the Drinfeld discriminant and the characteristic p valued measure associated to the Poincaré series.