Abstract:
The Gan-Gross-Prasad conjecture relates a special value of an L-function of two cuspidal automorphic representations to the non-vanishing of a certain period. The Ichino-Ikeda conjecture is a refinement of this conjecture. It roughly states that the absolute value of the square of the period in question can be expressed as a product of the special value of the L-function and a product of normalized local periods. However, in order to formulate this conjecture, one needs to assume that the representations in question are tempered everywhere, or else the convergence of the local periods is not guaranteed. In this talk, I will talk about my thesis result which allows one to relax the assumption that the representations are tempered everywhere, and explains how to extend the definition of the normalized local periods for places where the local components are given by principal series representations.