# On the residue method for period integrals

## TL;DR

This paper explores the residue method combined with Langlands-Shahidi theory to analyze period integrals on six spherical varieties, establishing links to automorphic L-functions and examining local multiplicities.

## Contribution

It introduces a novel approach by applying the residue method to multiple spherical varieties, connecting period integrals with automorphic L-functions and studying local multiplicities.

## Key findings

- Established relations between period integrals and automorphic L-functions for six spherical varieties.
- Analyzed local multiplicities in certain cases.
- Extended residue method applications to new classes of spherical varieties.

## Abstract

By applying the residue method for period integrals and Langlands-Shahidi's theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each spherical variety, we prove a relation between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.