Jiaqi Hou

activity

20242026

collaborators

5 papers

math.NT2026

$L^{q}$ -norm bounds for arithmetic eigenfunctions via microlocal Kakeya-Nikodym estimate

Jiaqi Hou, Xiaoqi Huang

Let $X$ be a compact arithmetic congruence hyperbolic surface, and let $ψ$ be an $L^{2}$ -normalized Hecke-Maass form on $X$ with sufficiently large spectral parameter $λ$ . We give a…

math.NT2025

Kakeya-Nikodym norms of Maass forms on $U (2, 1)$

Jiaqi Hou

Let $ψ$ be a Hecke-Maass form with a large spectral parameter on a compact arithmetic complex hyperbolic surface. We apply the amplification method to obtain a power saving over th…

math.NT2025

Weighted geodesic restrictions of arithmetic eigenfunctions

Jiaqi Hou, Xiaoqi Huang

Let $X$ be an arithmetic hyperbolic surface, $ψ$ a Hecke-Maass form, $ℓ$ a geodesic segment on $X$ , and $μ$ a Borel measure supported on $ℓ$ with dimension greater than 1/2.…

math.NT2024

Restrictions of Maass forms on $SL (2, C)$ to hyperbolic surfaces and geodesic tubes

Jiaqi Hou

Let $ψ$ be an $L^{2}$ -normalized Hecke-Maass form with a large spectral parameter $λ > 0$ on a compact arithmetic congruence hyperbolic 3-manifold $X=Γ\backslash\mathrm{SL}(2,\mathbb{C…

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…

Lq-norm bounds for arithmetic eigenfunctions via microlocal Kakeya-Nikodym estimate

Kakeya-Nikodym norms of Maass forms on U(2,1)

Weighted geodesic restrictions of arithmetic eigenfunctions

Restrictions of Maass forms on SL(2,C) to hyperbolic surfaces and geodesic tubes

A nonabelian circle method

$L^{q}$ -norm bounds for arithmetic eigenfunctions via microlocal Kakeya-Nikodym estimate

Kakeya-Nikodym norms of Maass forms on $U (2, 1)$

Restrictions of Maass forms on $SL (2, C)$ to hyperbolic surfaces and geodesic tubes