The doubling method in algebraic families
File(s)
Author(s)
Girsch, Johannes
Type
Thesis
Abstract
We define the doubling Zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that there exists an appropriate normalizing factor which allows us to construct gamma-factors for smooth families out of the functional equation. We prove that under certain hypothesis, specializing this gamma-factor at a point of the family yields the $\gamma$-factor defined by Piateski-Shapiro and Rallis. In the final chapter we begin to adapt the twisted doubling method due to Cai, Friedberg, Ginzburg and Kaplan to the setting of families.
Version
Open Access
Date Issued
2022-08-31
Date Awarded
01/02/2024
Advisor
Helm, David
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)