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


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