Geometric and Analytic Estimates

Abstract

In Chap. 1 and 2, we dealt at length with estimates concerning various coordinates on Pos_n and the volume on Pos_n. Here we come to deal with the metric itself, and the application of coordinate estimates to the convergence of certain Dirichlet series called Eisenstein series. Further properties of such series will then be treated in the next chapter. On the whole we follow Maass [Maa 71], Sect. 3, Sect. 7 and especially Sect. 10, although we make somewhat more efficient use of the invariant measure in Iwasawa coordinates, thereby introducing some technical simplifications.