An evaluation of the Ph. Hall function on rank 1 groups of Lie type

In 1936 Ph. Hall introduced the generalized $n$-th Eulerian function on finite groups and the associated function that is called the $n$-th Hall function. The values of the latter are estimated in the article for three of the four series of Lie type groups of rank 1. When $n=2$, these evaluations confirm the Wiegold conjecture for the groups.