Jiaqi Hou

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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 $I ¨ $ be an $L^{2}$ -normalized Hecke-Maass form on $X$ with sufficiently large spectral parameter $I^»$ . We give…

math.NT2025

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

Jiaqi Hou

Let $I ¨ $ be an $L^{2}$ -normalized Hecke-Maass form with a large spectral parameter $I^» > 0$ on a compact arithmetic congruence hyperbolic 3-manifold $X=Î\backslash\mathrm{SL}(2,\mathb…

math.NT2025

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

Jiaqi Hou

Let $I ¨ $ 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 t…

math.NT2025

Weighted geodesic restrictions of arithmetic eigenfunctions

Jiaqi Hou, Xiaoqi Huang

Let $X$ be an arithmetic hyperbolic surface, $I ¨ $ a Hecke-Maass form, $ℓ$ a geodesic segment on $X$ , and $I^¼$ a Borel measure supported on $ℓ$ with dimension greater than 1/2…

math.NT2024

A nonabelian circle method

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

We count integral quaternion zeros of $Î³_1^2 \pm \dots \pm Î³_n^2$, giving an asymptotic when $n \geq 9$ , and a likely near-optimal bound when $n = 8$ . To do so, we introduce a new, n…

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

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

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

Weighted geodesic restrictions of arithmetic eigenfunctions

A nonabelian circle method

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

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

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