Introduction to the relative trace formula of Guo-Jacquet

For zoom details please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

In the relative Langlands programme, we are interested in the relation between periods of automorphic representations and special values of L-functions. As one of the first interesting examples, Guo and Jacquet have proposed a conjecture generalising Waldspurger’s well-known theorem relating toric periods to central values of automorphic L-functions for $GL(2)$. A promising tool to attack this conjecture is the relative trace formula. Although the formula has not been established in full generality, its simple version has been used to prove some cases of Guo-Jacquet’s conjecture. In this talk, we shall introduce the background of their conjecture and survey some known results obtained via the relative trace formula. In the end, we shall also mention our study of some problems arising from this approach.