Local symmetric square L-functions for GL(2)

Abstract: In the influential work, Gelbart and Jacquet analyzed the integral representation for local symmetric square $L$-functions on $GL(2)$ at finite places based on the work of Shimura. In doing so, Gelbart and Jacquet explicitly constructed the local functorial lifting from $GL(2)$ to $GL(3)$. In this talk we present a natural way to define the $L$-function from the family of integrals for the space of good sections proposed by Piatetski-Shapiro and Rallis. We show that this analytic local $L$-function for an irreducible admissible representation of $GL(2)$ agrees with the corresponding symmetric square Artin $L$-function for its Langlnads parameter through the local Langlands correspondence.

number theoryrepresentation theory

Audience: researchers in the discipline

The 2020 Paul J. Sally, Jr. Midwest Representation Theory Conference

Series comments: The 44th Midwest Representation Theory Conference will address recent progress in the theory of representations for groups over non-archimedean local fields, and connections of this theory to other areas within mathematics, notably number theory and geometry.

In order to receive information on how to participate (to be sent out closer to the conference), please register by October 14 here: forms.gle/zFAnQBnuPGRnKzMr7