Explicit Constructions of Automorphic Forms: Theta Correspondence and Automorphic Descent

TL;DR

This paper discusses explicit methods for constructing automorphic representations, focusing on theta correspondence and automorphic descent, based on lectures from a 2022 IHES summer school on the Langlands program.

Contribution

It provides detailed explicit constructions of automorphic forms using theta correspondence and automorphic descent techniques, advancing practical understanding in the Langlands program.

Findings

Develops explicit construction methods for automorphic forms

Clarifies the role of theta correspondence in automorphic representation theory

Provides new examples and techniques for automorphic descent

Abstract

This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.