Title: An introduction to the Jacquet-Langlands correspondence and the relative trace formula

Abstract: Feigon and Whitehouse studied central values of triple L-functions averaged over newforms of weight 2 and prime level. In 2010 they proved some exact formulas applying the results of Gross and Kudla which link central values of triple L-functions to classical "periods". The aim of this series of lectures is to give a brief introduction to Jacquet's relative trace formula, and to explain how to generalize their results to modular forms of weight 2 and square-free levels. More specifically we will discuss:

1. cusp forms and representations of GL(2);

2. unitary representations on a quaternion algebra, and the Jacquet-Langlands correspondence;

3. Selberg trace formula through the “cocompact case”;

4. Jacquet's relative trace formula and its application to the central values of triple product L-functions.

Speaker: 管彬  (CUNY)

Time/Venue：

2019.5.29 2:30-4:30   B1044

2019.5.31  9:00-11:00   B1032