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Plancherel and Poisson summation formulae for a family of affine -bundles
Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu
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…
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…
Automorphic-twisted summation formulae for pairs of quadratic spaces
Miao Pam Gu
We prove a summation formula for pairs of quadratic spaces following the conjectures of Braverman-Kazhdan, Lafforgue, Ngô and Sakellaridis. We also give an expression of the local…
Factorization tests and algorithms arising from counting modular forms and automorphic representations
Miao Gu, Greg Martin
A theorem of Gekeler compares the number of non-isomorphic automorphic representations associated with the space of cusp forms of weight on to a simpler function of $k…