Introduction to the relative trace formulae of Guo-Jacquet

Abstract: 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.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October