We shall discuss some elementary combinatorial properties of the real analytic "Eisenstein Series" on the group SL(2) first discovered by Dirichlet in 1837. These properties, which originally led to the class number formula for quadratic number fields, form an essential component of the modern theory of "Eisenstein Series" in the context of Selberg and Langlands. A secondary aim of the talk is to clarify the historical record with respect to Dirichlet's contributions in this area.
Carlos J. Moreno