Automorphic Forms on Unitary Groups

TL;DR

This paper offers a detailed exploration of automorphic forms on unitary groups, emphasizing algebraicity results and related automorphic L-functions, expanding the understanding beyond classical groups.

Contribution

It provides an in-depth treatment of automorphic forms on unitary groups, focusing on algebraicity and automorphic L-functions, which advances the theoretical framework in this area.

Findings

Enhanced understanding of automorphic forms on unitary groups

Results on algebraicity of automorphic forms

Discussion of automorphic L-functions in this context

Abstract

This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a view toward algebraicity results. I also discuss related aspects of automorphic $L$-functions in the setting of unitary groups.