|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||The standard \(L\)-function for \(G_2\): a "new way"|
|Affiliation:||Ben-Gurion University of the Negev|
|Date:||Thursday, October 2|
|Time/Room:||4:30pm - 5:30pm/S-101|
We consider a Rankin-Selberg integral representation of a cuspidal (not necessarily generic) representation of the exceptional group \(G_2\). Although the integral unfolds with a non-unique model, it turns out to be Eulerian and represents the standard \(L\)-function of degree 7. We discuss a general approach to the integrals with non-unique models. The integral can be used to describe the representations of \(G_2\) for which the (twisted) \(L\)-function has a pole as functorial lifts. This is a joint work with Avner Segal.