Eisenstein series and cusp counting in hyperbolic manifolds

We study the Eisenstein series in a complete infinite volume hyperbolic manifold. We show that each full rank cusp corresponds to a cohomology class via the Eisenstein series construction. Moreover, by computing the intertwining operator, we show that different cusps give rise to linearly independent classes. As a consequence, the number of full rank cusps is bounded by the dimension of the cohomology group. This is joint work with Beibei Liu.