Titles and Abstracts

Ellen Eischen, University of Oregon

Title: p-adic L-functions and Eisenstein series on unitary groups

Abstract: I will discuss a construction of p-adic L-functions, with a focus on p-adic L- functions attached to cuspidal automorphic representations of unitary groups. I will highlight how this construction relates to more familiar ones of Serre, Katz, and Hida, and I will emphasize the role of properties of certain automorphic forms (analogous to the role played by modular forms in their work). This is joint work with Michael Harris, Jian-Shu Li, and Christopher Skinner.

Abhishek Parab, Purdue University

Title: Absolute convergence of the Twisted Arthur-Selberg Trace Formula

Abstract: We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven in many useful cases including when the group is split. It extends the work of Finis-Lapid (and Muller, spectral side) in the non-twisted setting. In the end, we will give an application towards residues of Rankin-Selberg L-functions.

Chen Wan, Institute for Advanced Studies

Title: The local trace formula for the Ginzburg-Rallis model and the generalized Shalika model

Abstract: We will first discuss a local trace formula for the Ginzburg-Rallis model. This trace formula allows us to prove a multiplicity formula for the Ginzburg-Rallis model, which implies that the summation of the multiplicities on every tempered Vogan L-packet is always equal to 1. Then we will talk about an analogy of this trace formula for the generalized Shalika model, which implies that the multiplicity for the generalized Shalika model is a constant on every discrete Vogan L-packet.