PERIOD INTEGRALS OF AUTOMORPHIC FORMS

This work concerns some problems in the theory of automorphic forms.The PI proposes a study of the period integrals of automorphic forms through two approaches. One is through developing the relative trace formula, the other is using a period transference principle based on the Rankin-Selberg method and the explicit realization of Langlands functoriality.This research is in the area of number theory. Number theory has its historical roots in the study of natural numbers. It is among the oldest branches of mathematics. Within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems