  The Test Function Conjecture due to Haines and Kottwitz predicts that the
geometric Bernstein center is a source of test functions required by the
Langlands-Kottwitz method for expressing the local semisimple Hasse-Weil zeta
function of a Shimura variety in terms of automorphic L-functions. Haines and
Rapoport found an explicit formula for such test functions in the Drinfeld case
with pro-p Iwahori level structure.
  This article generalizes the Haines-Rapoport formula for the Drinfeld case to
a broader class of split groups. The main theorem presents a new formula for
test functions with pro-p Iwahori level structure, which can be computed
through some combinatorics on Coxeter groups. Explicit descriptions of the test
function in certain low-rank general linear and symplectic group examples are
included.
