Zeros and central values of automorphic L-functions

It has long been observed in the study of automorphic L-functions that an aptly chosen family of L-functions often serves as a ready conduit leading to illuminating revelations about its individual members. Indeed, this method is so widely applicable that its significance exceeds mere technical concern. There is much evidence that a suitable family may be the natural context in which questions should be considered and answered. One particularly striking example of this phenomenon is the work of N. Katz and P. Sarnak on the zeros of zeta functions and symmetry. The authors demonstrated that the distribution of low lying zeros of L-functions belonging to certain families is governed by symmetries associated with the family.;The philosophy emerging from Katz-Sarnak has given rise to a series of investigations concerning the zeros of automorphic L-functions for various families. Of particular interest, for example, is the work of H. Iwaniec, W. Luo and P. Sarnak, in which the authors demonstrated that Hecke L-functions attached to holomorphic forms exhibit the predicted symmetries. In the first part of this dissertation, our investigation, which originates from the same general motivation, shows that the distribution of zeros of Hecke L-functions attached to Maali forms confirms the philosophy of Katz-Sarnak.;In a separate direction, all known subconvexity bounds concerning the central value of L-functions proceed from investigations of suitable families as well. In the second part of this dissertation, we present a result for the Hecke L-functions attached to holomorphic forms for SL2Z of weight k. The bound k13+e which we are able to obtain, is comparable to established results for Maass forms in the eigenvalue aspect as well as holomorphic forms in the level aspect.