Jayce R. Getz

activity

20132026

most citedSecondary terms in asymptotics for the number of zeros of quadratic forms over number fields

13 citations · 27 across the 19 of their papers we have counts for

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22 papers · 1 filter

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.NT2025

The $ρ$ -Fourier transform

Jayce R. Getz, Armando Gutiérrez Terradillos, Farid Hosseinijafari +4

Let $G$ be a reductive group over a local field $F$ and let $ρ :^{L} G \to GL_{V_{ρ}} (C)$ be a representation of its $L$ -group satisfying suitable assumptions. Braver…

math.NT2025

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 assumptio…

math.NT2025

Triple product $L$ -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 $L$ -functions hold. Further, we explain how these analyt…

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…

math.NT2022

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…

math.NT2021★ 1 cited

Schubert Eisenstein series and Poisson summation for Schubert varieties

YoungJu Choie, Jayce R. Getz

The first author and Bump defined Schubert Eisenstein series by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of $\mathr…

math.NT2021

Harmonic analysis on certain spherical varieties

Jayce R. Getz, Chun-Hsien Hsu, Spencer Leslie

Braverman and Kazhdan proposed a conjecture, later refined by Ngô and broadened to the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varietie…

math.NT2020★ 1 cited

The Fourier transform for triples of quadratic spaces

Jayce R. Getz, Chun-Hsien Hsu

Let $V_{1}, V_{2}, V_{3}$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $Q_{1}, Q_{2}, Q_{3}$ , res…

math.NT2019★ 1 cited

On triple product L-functions

Jayce R. Getz

Let $π = π_{1} \otimes π_{2} \otimes π_{3}$ be a unitary cuspidal automorphic representation of $GL_{3}^{3} (A_{F})$ where $F$ is a number field. Assume that $π$ is everywhere t…

math.NT2017

A summation formula for triples of quadratic spaces

Jayce R. Getz, Baiying Liu

Let $V_{1}, V_{2}, V_{3}$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $Q_{1}, Q_{2}, Q_{3}$ , res…

math.NT2017★ 4 cited

A refined Poisson summation formula for certain Braverman-Kazhdan spaces

Jayce R. Getz, Baiying Liu

Braverman and Kazhdan introduced influential conjectures generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Lan…

math.NT2017★ 13 cited

Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields

Jayce Robert Getz

Let $Q$ be a nondegenerate quadratic form on a vector space $V$ of even dimension $n$ over a number field $F$ . Via the circle method or automorphic methods one can give good estima…

math.NT2017★ 1 cited

An approach to nonsolvable base change and descent

Jayce R. Getz

We present a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F…

math.NT2017

Twisted relative trace formulae with a view towards unitary groups

Jayce R. Getz, Eric Wambach

We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula…

math.NT2015

Algebraic cycles and Tate classes on Hilbert modular varieties

Jayce R. Getz, Heekyoung Hahn

Let $E / Q$ be a totally real number field that is Galois over $Q$ , and let $π$ be a cuspidal, nondihedral automorphic representation of $\mathrm{GL}_2(\mathbb{A}_E…

math.NT2015

Nonabelian Fourier transforms for spherical representations

Jayce R. Getz

Braverman and Kahzdan have introduced an influential conjecture on local functional equations for general Langlands $L$ -functions. It is related to L. Lafforgue's equally influenti…

math.NT2014★ 2 cited

Invariant four-variable automorphic kernel functions

Jayce R. Getz

Let $F$ be a number field, let $A_{F}$ be its ring of adeles, and let $g_{1}, g_{2}, h_{1}, h_{2} \in GL_{2} (A_{F})$ . Previously the author provided an absolutely converg…

math.NT2014

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

Jayce R. Getz

Let $F$ be a number field and let $A_{F}$ be its ring of adeles. Let $B$ be a quaternion algebra over $F$ and let $ν : B \to F$ be the reduced norm. Consider the reductive mon…

math.NT2014★ 2 cited

A general simple relative trace formula and a relative Weyl law

Jayce R. Getz, Heekyoung Hahn

In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl law.

math.NT2013★ 2 cited

A nonabelian trace formula

Jayce R. Getz, P. Edward Herman

Let $E / F$ be an extension of number fields with $Gal (E / F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descen…

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

The ρ-Fourier transform

Modulation groups

Triple product L-functions and the Ramanujan conjecture

On triple product L-functions and the fiber bundle method

A nonabelian circle method

Summation formulae for quadrics

Schubert Eisenstein series and Poisson summation for Schubert varieties

Harmonic analysis on certain spherical varieties

The Fourier transform for triples of quadratic spaces

On triple product L-functions

A summation formula for triples of quadratic spaces

A refined Poisson summation formula for certain Braverman-Kazhdan spaces

Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields

An approach to nonsolvable base change and descent

Twisted relative trace formulae with a view towards unitary groups

Algebraic cycles and Tate classes on Hilbert modular varieties

Nonabelian Fourier transforms for spherical representations

Invariant four-variable automorphic kernel functions

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

A general simple relative trace formula and a relative Weyl law

A nonabelian trace formula

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

The $ρ$ -Fourier transform

Triple product $L$ -functions and the Ramanujan conjecture

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