This PhD thesis consists of a summary and five papers which all deal with asymptotic problems on certain homogeneous spaces. In Paper I we prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. All our results are given with precise estimates on the rates of convergence to equidistribution. Papers II and III are concerned with statistical problems on the space of n-dimensional lattices of covolume one. In Paper II we study the distribution of lengths of non-zero lattice vectors in a random lattice of large dimension. We prove that these lengths, when properly normalized, determine a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. In Paper III we complement this result by proving that the asymptotic distribution of the angles between the shortest non-zero vectors in a random lattice is that of a family of independent Gaussians. In Papers IV and V we investigate the value distribution of the Epstein zeta function along the real axis. In Paper IV we determine the asymptotic value distribution and moments of the Epstein zeta function to the right of the critical strip as the dimension of the underlying space of lattices tends to infinity. In Paper V we determine the asymptotic value distribution of the Epstein zeta function also in the critical strip. As a special case we deduce a result on the asymptotic value distribution of the height function for flat tori. Furthermore, applying our results we discuss a question posed by Sarnak and Strömbergsson as to whether there in large dimensions exist lattices for which the Epstein zeta function has no zeros on the positive real line.

The use of materialized views in a data warehouse installation is a common tool to speed up mostly aggregation queries. The problems coming along with materialized aggregate views have triggered a huge variety of proposals, such as picking the optimal set of aggregation combinations, transparently rewriting user queries to take advantage of the summary data, or synchronizing pre-computed summary data as soon as the base data changes. The paper focuses on the problem of view selection in the context of distributed data warehouse architectures. While much research was done with regard to the view selection problem in the central case, we are not aware to any other work discussing the problem of view selection in distributed data warehouse systems. The paper proposes an extension of the concept of an aggregation lattice to capture the distributed semantics. Moreover, we extend a greedy-based selection algorithm based on an adequate cost model for the distributed case. Within a performance study, we finally compare our findings with the approach of applying a selection algorithm locally to each node in a distributed warehouse environment.