7 papers
Plancherel and Poisson summation formulae for a family of affine -bundles
Jayce R. Getz, Miao, Miao Pam Gu +2
We prove a Plancherel formula for a family of affine -bundles. As an application, we construct Fourier transforms and asymptotic Schwartz spaces for the family. We then prove th…
The -Fourier transform
Jayce R. Getz, Armando Gutiérrez Terradillos, Farid Hosseinijafari +4
Let be a reductive group over a local field and let be a representation of its -group satisfying suitable assumptions. Brav…
Modulation groups
Jayce R. Getz, Armando Gutiérrez Terradillos, Farid Hosseinijafari +6
Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumpti…
Triple product -functions and the Ramanujan conjecture
Jayce R. Getz, Heekyoung Hahn, HaoYun Yao
We prove that the Ramanujan conjecture is true under the assumption that the expected analytic properties of triple product -functions hold. Further, we explain how these analyt…
On triple product -functions and the fiber bundle method
Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu +1
We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product -function times a product of -functions with known analytic properti…
Summation formulae for quadrics
Jayce R. Getz
We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key nove…