Please register here: https://zoom.us/meeting/register/tJEtcuuvqTksHdfsLV9ZiYeWaHDdqnotA5-5 . In this talk, we will mainly discuss holomorphic continuation of (complete) adjoint $L$-functions for GL$(n,F)$ where $n\leq 4$ and $F$ is a number field. To obtain the continuation, we generalize Jacquet-Zagier's trace formula to GL$(n).$ Through this trace formula one can write adjoint L-functions as linear combinations of certain Artin $L$-series and $L$-functions defined by Langlands-Shahidi method and Mellin transforms of Rankin-Selberg periods for non-discrete automorphic representations. A further application towards "Arithmetic Sato-Tate" for GL$(3)$ will be provided as well.

An introductory lecture for this seminar talk can be seen here: https://youtu.be/_cCMW2LbX1g .
Slides for the introductory lecture can be found here.