# A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula

Published

Journal Article

© 2020 by Johns Hopkins University Press. Let F be a number field and let AF be its ring of adeles. Let B be a quaternion algebra over F and let ν: B → F be the reduced norm. Consider the reductive monoid M over F whose points in an F-algebra R are given by (Formula Presented). Motivated by an influential conjecture of Braverman and Kazhdan we prove a summation formula analogous to the Poisson summation formula for certain spaces of functions on the monoid. As an application, we define new zeta integrals for the Rankin-Selberg L-function and prove their basic properties. We also use the formula to prove a nonabelian twisted trace formula, that is, a trace formula whose spectral side is given in terms of automorphic representations of the unit group of M that are isomorphic (up to a twist by a character) to their conjugates under a simple nonabelian Galois group.

### Full Text

### Duke Authors

### Cited Authors

- Getz, JR

### Published Date

- October 1, 2020

### Published In

### Volume / Issue

- 142 / 5

### Start / End Page

- 1371 - 1407

### Electronic International Standard Serial Number (EISSN)

- 1080-6377

### International Standard Serial Number (ISSN)

- 0002-9327

### Digital Object Identifier (DOI)

- 10.1353/ajm.2020.0035

### Citation Source

- Scopus