Math @ Duke

Publications [#353052] of Jayce R. Getz
Papers Published
 Getz, JR, A summation formula for the RankinSelberg monoid and a nonabelian trace formula,
American Journal of Mathematics, vol. 142 no. 5
(October, 2020),
pp. 13711407 [doi]
(last updated on 2021/11/30)
Abstract: 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 Falgebra 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 RankinSelberg Lfunction 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.


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