Chun-Hsien Hsu

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20242026

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math.NT2026

Plancherel and Poisson summation formulae for a family of affine $Ψ$ -bundles

Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu

We prove a Plancherel formula for a family of affine $Ψ$ -bundles. As an application, we construct Fourier transforms and asymptotic Schwartz spaces for the family. We then prove th…

math.NT2026

Schwartz spaces on L-monoids: non-Archimedean

Chun-Hsien Hsu, HaoYun Yao

We complete the Braverman-Kazhdan-Ngô program over non-Archimedean local fields assuming local Langlands conjecture for tempered representations and a natural assumption on the $γ$ …

math.NT2026

Geometrization of summation formulae for quadrics

Chun-Hsien Hsu

We geometrize the Poisson summation formula for the zero locus of a split quadratic form in an even number of variables over number fields. We do so by making explicit the relation…

math.NT2025

On triple product $L$ -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 $L$ -function times a product of $L$ -functions with known analytic properti…

math.NT2024

A nonabelian circle method

Nuno Arala, Jayce R. Getz, Jiaqi Hou +3

We count integral quaternion zeros of $γ_{1}^{2} \pm \dots \pm γ_{n}^{2}$ , giving an asymptotic when $n \geq 9$ , and a likely near-optimal bound when $n = 8$ . To do so, we introduce a new, non…

Plancherel and Poisson summation formulae for a family of affine Ψ-bundles

Schwartz spaces on L-monoids: non-Archimedean

Geometrization of summation formulae for quadrics

On triple product L-functions and the fiber bundle method

A nonabelian circle method

Plancherel and Poisson summation formulae for a family of affine $Ψ$ -bundles

On triple product $L$ -functions and the fiber bundle method