Periods and theta correspondence

摘要

1. Introduction One important application of the theory of theta correspondence is that it gives a way of relating certain periods of one member of a dual pair with certain periods on the other member of the dual pair. It thus serves as a complement to the method of the relative trace formula. While the relative trace formula may have a wider range of applicability, one advantage of the theta correspondence approach for such problems is that the analysis of the local and global period problems are often completely parallel, so that one tends to obtain quite complete results at both the local and global level with essentially the same amount and type of work.